{"id":28893,"date":"2023-01-09T12:14:41","date_gmt":"2023-01-09T06:44:41","guid":{"rendered":"https:\/\/ccssanswers.com\/?p=28893"},"modified":"2023-01-10T09:17:15","modified_gmt":"2023-01-10T03:47:15","slug":"big-ideas-math-answers-grade-7-chapter-7","status":"publish","type":"post","link":"https:\/\/ccssanswers.com\/big-ideas-math-answers-grade-7-chapter-7\/","title":{"rendered":"Big Ideas Math Answers Grade 7 Chapter 7 Probability"},"content":{"rendered":"<p>In order to solve real-life mathematical problems, students must understand the concept behind the question. You have to know what is probability. This is the most interesting chapter among all the grade 7 chapters. Download Free Pdf of <a href=\"https:\/\/ccssanswers.com\/big-ideas-math-answers-grade-7\/\">Big Ideas Math Answers Grade 7<\/a> Chapter 7 Probability to practice the exercise and homework problems.<\/p>\n<h2>Big Ideas Math Book 7th Grade Answer Key Chapter 7 Probability<\/h2>\n<p>Improve your math skills with the help of Big Ideas Math Answers Grade 7 Chapter 7 Probability. Unlimited practice with all the question and answers along with the practice test. It is mandatory to practice with the Big Ideas Math Answer Key for Grade 7 Chapter 7 Probability to secure maximum marks in the exams. Check out the links given the below sections before you start your preparation.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<ul>\n<li><a href=\"#Probability_STEAM_Video\/Performance_Task\">Probability STEAM Video\/Performance Task<\/a><\/li>\n<li><a href=\"#Probability_Getting_Ready_for_Chapter_7\">Probability Getting Ready for Chapter 7<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 1 Probability<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_7.1_Probability\">Lesson 7.1 Probability<\/a><\/li>\n<li><a href=\"#Probability_Homework_&amp;_Practice_7.1\">Probability Homework &amp; Practice 7.1<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 2 Experimental and Theoretical Probability<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_7.2_Experimental_and_Theoretical_Probability\">Lesson 7.2 Experimental and Theoretical Probability<\/a><\/li>\n<li><a href=\"#Experimental_and_Theoretical_Probability_Homework_&amp;_Practice_7.2\">Experimental and Theoretical Probability Homework &amp; Practice 7.2<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 3 Compound Events<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_7.3_Compound_Events\">Lesson 7.3 Compound Events<\/a><\/li>\n<li><a href=\"#Compound_Events_Homework_&amp;_Practice_7.3\">Compound Events Homework &amp; Practice 7.3<\/a><\/li>\n<\/ul>\n<p><strong>Lesson: 4 Simulations<\/strong><\/p>\n<ul>\n<li><a href=\"#Lesson_7.4_Simulations\">Lesson 7.4 Simulations<\/a><\/li>\n<li><a href=\"#Simulations_Homework_&amp;_Practice_7.4\">Simulations Homework &amp; Practice 7.4<\/a><\/li>\n<\/ul>\n<p><strong>Chapter: 7 &#8211; Probability\u00a0<\/strong><\/p>\n<ul>\n<li><a href=\"#Probability_Connecting_Concepts\">Probability Connecting Concepts<\/a><\/li>\n<li><a href=\"#Probability_Chapter_Review\">Probability Chapter Review<\/a><\/li>\n<li><a href=\"#Probability_Practice_Test\">Probability Practice Test<\/a><\/li>\n<li><a href=\"#Probability_Cumulative_Practice\">Probability Cumulative Practice<\/a><\/li>\n<\/ul>\n<h3><a id=\"Probability_STEAM_Video\/Performance_Task\"><\/a>Probability STEAM Video\/Performance Task<\/h3>\n<p><strong>STEAM Video<\/strong><\/p>\n<p>Massively Multiplayer Rock Paper Scissors.<br \/>\nYou can use experimental probability to describe the percent of times that you win, lose, or tie in Rock Paper Scissors. Describe a real-life situation where it is helpful to describe the percent of times that a particular outcome occurs.<\/p>\n<p>Watch the STEAM Video \u201cMassively Multiplayer Rock Paper Scissors.\u201dThen answer the following questions.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28895\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 1\" width=\"538\" height=\"289\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-1.png 538w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-1-300x161.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><br \/>\n1. The table shows the ways that you can win, lose, or tie in Rock Paper Scissors. You and your opponent throw the signs for rock, paper, or scissors at random. What percent of the time do you expect to win? lose? tie?<br \/>\n2. You play Rock Paper Scissors 15 times. About how many times do you expect to win? Explain your reasoning.<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Fair and Unfair Carnival Games<br \/>\nAfter completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28896\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 2\" width=\"262\" height=\"331\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-2.png 262w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-2-237x300.png 237w\" sizes=\"(max-width: 262px) 100vw, 262px\" \/><br \/>\nYou will be given information about a version of Rock Paper Scissors used at a carnival. Then you will be asked to design your own &#8220;unfair&#8221; carnival game using a spinner or a number cube, and test your game with a classmate.<br \/>\nIn what ways can a game of chance be considered fair? unfair? Explain your reasoning.<\/p>\n<h3><a id=\"Probability_Getting_Ready_for_Chapter_7\"><\/a>Probability Getting Ready for Chapter 7<\/h3>\n<p><strong>Chapter Exploration<\/strong><br \/>\nWork with a partner.<br \/>\n1. Play Rock Paper Scissors 30 times. Tally your results in the table.<br \/>\n2. How many possible results are there?<br \/>\n3. Of the possible results, in how many ways can Player A win? In how many ways can Player B win? In how many ways can there be a tie?<br \/>\n4. Is one of the players more likely to win than the other player? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28897\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 3\" width=\"455\" height=\"344\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-3.png 455w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-3-300x227.png 300w\" sizes=\"(max-width: 455px) 100vw, 455px\" \/><\/p>\n<p><strong>Vocabulary<\/strong><br \/>\nThe following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.<br \/>\nprobability<br \/>\ntheoretical probability<br \/>\nsimulation<br \/>\nrelative frequency<br \/>\nsample space<br \/>\nexperimental probability<br \/>\ncompound event<\/p>\n<h3><a id=\"Lesson_7.1_Probability\"><\/a>Lesson 7.1 Probability<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Determining Likelihood<br \/>\nWork with a partner. Use the spinners shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28898\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 1\" width=\"383\" height=\"198\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-1.png 383w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-1-300x155.png 300w\" sizes=\"(max-width: 383px) 100vw, 383px\" \/><br \/>\na. For each spinner, determine which numbers you are more likely to spin and which numbers you are less likely to spin. Explain your reasoning.<br \/>\nb. Spin each spinner 20 times and record your results in two tables. Do the data support your answers in part(a)? Explain why or why not.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28899\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 2\" width=\"602\" height=\"237\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-2.png 602w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-2-300x118.png 300w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><br \/>\nc. How can you use percents to describe the likelihood of spinning each number? Explain.<br \/>\nAnswer:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28900\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 3\" width=\"189\" height=\"189\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-3.png 189w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-3-150x150.png 150w\" sizes=\"(max-width: 189px) 100vw, 189px\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nYou randomly choose one of the tiles shown from a hat.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28901\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-4.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 4\" width=\"159\" height=\"177\" \/><br \/>\na. How many possible outcomes are there?<\/p>\n<p>Answer:<br \/>\nThere are 5 number of unique possible outcomes<br \/>\nThey are { A,B,C,D,E}<br \/>\nTherefore, there are 5 possible outcomes for the event.<\/p>\n<p>b. What are the favorable outcomes of choosing a vowel ?<\/p>\n<p>Answer:<br \/>\nThere are 2 favorable outcomes of choosing an vowel<br \/>\nThey are {A,E}<br \/>\nTherefore, there are 2 favorable outcomes of choosing an vowel.<\/p>\n<p>C. In how many ways can choosing a consonant occur?<br \/>\nAnswer: 3 ways<\/p>\n<p>Explanation:<br \/>\nThere are 3 unique consonant tiles. They are {B,C,D}<\/p>\n<p><strong>Describe the likelihood of the event given its probability.<\/strong><br \/>\nQuestion 2.<br \/>\nThe probability that you land a jump on a snowboard is \\(\\frac{1}{10}\\).<br \/>\nAnswer:<br \/>\nGiven, Probability of landing a jump on snowboard = 1\/10 = 0.1<br \/>\nSo, the likelihood of the event of jumping on to the snowboard after every jump is 1 out of 10 times.<\/p>\n<p>Question 3.<br \/>\nThere is a 100% chance that the temperature will be less than 120\u00b0F tomorrow.<br \/>\nAnswer:<br \/>\nCertain event .<br \/>\nGiven that , there is 100% chance that the temperature will be less than 120<sup>0\u00a0<\/sup>F tomorrow.<br \/>\nThe probability for a certain event is P(E)= 1.<br \/>\nSo, the probability that the temperature being 120<sup>0\u00a0<\/sup>F tomorrow is 1.<\/p>\n<p>Question 4.<br \/>\nYou attempt three-point shots on a basketball court and record the number of made and missed shots. Describe the likelihood of each event.\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28902\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-5.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 5\" width=\"166\" height=\"70\" \/><br \/>\n\u0307\u0307a. You make your next shot.<br \/>\nb. You miss your next shot.<br \/>\nAnswer:<br \/>\na.<br \/>\nExplanation:<br \/>\nTotal number of shots = 15<br \/>\nFrequency of shots made = 9<br \/>\nThe likelihood of making next shot is<br \/>\nShots made\/ Total = 9\/15=0.6<br \/>\nSo, the next shot is likely to occur<\/p>\n<p>b.<br \/>\nExplanation:<br \/>\nTotal number of shots = 15<br \/>\nFrequency of missed shots = 6<br \/>\nThe likelihood of the next shot will miss is shots missed\/ Total =6\/15 0.4<br \/>\nSo, the next shot is not likely to occur.<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 5.<br \/>\n<strong>IDENTIFYING OUTCOMES<\/strong><br \/>\nYou roll a number cube. What are the possible outcomes?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28903\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-6.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 6\" width=\"123\" height=\"132\" \/><\/p>\n<p>Answer: 6<br \/>\nA cube has 6 faces .<br \/>\nThey are {1,2,3,4,5,6} .<br \/>\nThere are 6 possible outcomes.<br \/>\nTherefore , there are 6 possible outcomes for a cube.<\/p>\n<p>Question 6.<br \/>\n<strong>USING RELATIVE FREQUENCIES<\/strong><br \/>\nA bag contains only red marbles and blue marbles. You randomly draw a marble from the bag and replace it. The table shows the results of repeating this experiment. Find the likelihood of each event.\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28904\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-7.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 7\" width=\"133\" height=\"101\" \/><br \/>\na. The next marble you choose is red. \u0307\u0307<br \/>\nb. The next marble you choose is neither red nor blue.<br \/>\nAnswer:<\/p>\n<p>a.<br \/>\nExplanation:<br \/>\nTotal number of balls = 42<br \/>\nNumber of red balls = 21<br \/>\nThe likelihood of drawing the red marble in the next turn=<br \/>\nNumber of red balls\/ Total number of balls<br \/>\n= 21\/42 =0.5<br \/>\nThere is only 50% chance of chance of drawing a red ball in the next turn<br \/>\nSo, the likelihood of the event is may or ,ay not occur evenly.<\/p>\n<p>b.The likelihood of drawing neither red nor blue ball is 0<br \/>\n0%= Impossible<br \/>\nBecause, there are only red and blue marbles<br \/>\nSo, it is impossible to draw another ball other than red and blue.<br \/>\nTherefore, the likelihood of the event is cannot occur<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 7.<br \/>\nThe table shows the number of days you have a pop quiz and the number of days you do not have a pop quiz in three weeks of school. How many days can you expect to have a pop quiz during a 180-day school year? Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28905\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-8.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 8\" width=\"190\" height=\"72\" \/><br \/>\nAnswer:<br \/>\nTotal number of days for pop quiz for 3 weeks = 2<br \/>\nTotal frequency = 15<br \/>\nNow, the number of times to have a pop quiz in 180 days be x<br \/>\nTotal number of days =180<br \/>\n2\/15 = x\/180<br \/>\n15x = 360<br \/>\nx =\u00a0 360\/ 15<br \/>\nx = 24<br \/>\nTherefore, we can expect 24 days to have a pop quiz during a 180-day school year.<\/p>\n<p>Question 8.<br \/>\nIn a football game, the teams pass the ball on 40% of the plays. Of the passes thrown, greater than 75% are completed. You watch the film of a randomly chosen play. Describe the likelihood that the play results in a complete pass. Explain your reasoning.<br \/>\nAnswer:<br \/>\nGiven ,<br \/>\nThe team pass the ball on 40% of the plays<br \/>\nAnd also, 75% are completed<br \/>\n75% = 0.75<br \/>\nTherefore 75% = 3\/4<br \/>\nTherefore , the likelihood is likely to happen of the plays results in a complete pass = 0.34<\/p>\n<h3><a id=\"Probability_Homework_&amp;_Practice_7.1\"><\/a>Probability Homework &amp; Practice 7.1<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>An account earns simple interest. Find the interest earned.<\/strong><br \/>\nQuestion 1<br \/>\n$700 at 3% for 4 years<br \/>\nAnswer: $84<br \/>\nThe formula for simple interest= Principal x rate x time<br \/>\nI = P x r x t<br \/>\n= $700 x0.03 x 4 =$84<br \/>\nTherefore , the interest earned =\u00a0 $84<\/p>\n<p>Question 2.<br \/>\n$650 at 2% for 6 years<br \/>\nAnswer: $78<br \/>\nThe formula for simple interest= Principal x rate x time<br \/>\nI = P x r x t<br \/>\n= $650 x0.02 x 6 =$78<br \/>\nTherefore , the interest earned =\u00a0 $78<\/p>\n<p>Question 3.<br \/>\n$480 at 1.5% for 5 years<br \/>\nAnswer: $36<br \/>\nThe formula for simple interest= Principal x rate x time<br \/>\nI = P x r x t<br \/>\n= $480 x0.015 x 5 =$36<br \/>\nTherefore , the interest earned =\u00a0 $36<\/p>\n<p>Question 4.<br \/>\n$1200 at 2.8% for 30 months<br \/>\nAnswer: $84<br \/>\nThe formula for simple interest= Principal x rate x time<br \/>\nI = P x r x t<br \/>\n= $1200 x0.028 x 2.5 =$84<br \/>\nTherefore , the interest earned =\u00a0 $84<\/p>\n<p><strong>Write the indicated ratio. Then find and interpret the value of the ratio.<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28906\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-9.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 9\" width=\"207\" height=\"197\" \/><br \/>\nQuestion 5.<br \/>\nrolled oats : chopped peanuts<br \/>\nAnswer:<br \/>\n2 : 1\/2<br \/>\n2\/1 : 1\/2<br \/>\nMultiplying with 2<br \/>\n2\/1 x 2 : 1\/2 x 2<br \/>\n4\/2 : 2\/4<br \/>\n2\/1 : 1\/2<br \/>\n2\/1 x 2 : 1\/2:2<br \/>\n4 : 1<br \/>\nTherefore, the value of ratio = 4: 1<\/p>\n<p>Question 6.<br \/>\nsunflower seeds : pumpkin seeds<br \/>\nAnswer:<br \/>\n1\/3 :1\/4<br \/>\nMultiplying with 12<br \/>\n1\/3 x 12 : 1\/4 x 12<br \/>\n12\/36 : 12\/ 48<br \/>\n1\/3: 1 \/4<br \/>\n1\/3 x 12 : 1\/4 x12<br \/>\n12\/3 : 12\/4<br \/>\n4 : 3<br \/>\nTherefore, the ratio = 4 : 3<\/p>\n<p>Question 7.<br \/>\npumpkin seeds : rolled oats<br \/>\nAnswer:<br \/>\n1\/4 :2<br \/>\nOn multiplying with 4<br \/>\n1\/4 x 4 : 2\/1 x 4<br \/>\n4\/16 : 8\/4<br \/>\n1\/4: 2<br \/>\n1\/4 x 4 : 2 x 4<br \/>\n1 : 8<br \/>\nTherefore , ratio = 1:8<\/p>\n<p><strong>Solve the inequality. Graph the solution.<\/strong><br \/>\nQuestion 8.<br \/>\nx + 5 &lt; 9<br \/>\nAnswer: x&lt;4<\/p>\n<p>Explanation:<br \/>\nx + 5 &lt; 9<br \/>\n=x &lt; 9-5<br \/>\nx&lt;4<br \/>\nSo, the inequality form = x&lt;4<br \/>\nGraph:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-36107\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-3.jpg\" alt=\"\" width=\"242\" height=\"180\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-3.jpg 566w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-3-300x222.jpg 300w\" sizes=\"(max-width: 242px) 100vw, 242px\" \/><\/p>\n<p>Question 9.<br \/>\nb &#8211; 2 \u2265 &#8211; 7<br \/>\nAnswer: b\u2265-5<\/p>\n<p>Explanation:<br \/>\nb &#8211; 2 \u2265 &#8211; 7<br \/>\n= b \u2265 -7+2<br \/>\n= b\u2265-5<br \/>\nGraph:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-36106\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-2.jpg\" alt=\"\" width=\"224\" height=\"150\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-2.jpg 564w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-2-300x201.jpg 300w\" sizes=\"(max-width: 224px) 100vw, 224px\" \/><\/p>\n<p>Question 10.<br \/>\n1 &gt; &#8211; \\(\\frac{w}{3}\\)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n6 \u2264 &#8211; 2g<br \/>\nAnswer: g\u2264 -3<\/p>\n<p>Explanation:<br \/>\n= g\u2264 6\/-3<br \/>\n= g\u2264 -3<br \/>\nThe inequality = g\u2264 -3<br \/>\nGraph:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-36105\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-1.jpg\" alt=\"\" width=\"235\" height=\"177\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-1.jpg 565w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-1-300x225.jpg 300w\" sizes=\"(max-width: 235px) 100vw, 235px\" \/><\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>DETERMINING LIKELIHOOD<\/strong> Determine which numbers you are more likely to spin and which numbers you are less likely to spin. Explain your reasoning. (See Exploration 1, p. 283.)<br \/>\nQuestion 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28907\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-10.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 10\" width=\"183\" height=\"160\" \/><\/p>\n<p>Answer:<br \/>\nThe spinner is divided into 6 parts (unequal)<br \/>\nThey are numbered as {1,2,3,4,5,6}<br \/>\nThe numbers {2,4,5} are more likely to happen<br \/>\nBecause, they occupy more space than remaining.<br \/>\nAnd , the numbers {1,3,6] are less likely to happen<br \/>\nBecause , they occupy less space .<\/p>\n<p>Question 13.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28908\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-11.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 11\" width=\"174\" height=\"164\" \/><br \/>\nAnswer:<br \/>\nThe spinner is divided into 4 equal parts<br \/>\nThe 4 parts are numbered as {1,2,3,4}<br \/>\nSo, each number have equal chance of spinning<br \/>\nSuch events are also called as equally likely happen events.<\/p>\n<p><strong>IDENTIFYING OUTCOMES<\/strong> You spin the spinner shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28909\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-12.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 12\" width=\"122\" height=\"140\" \/><br \/>\nQuestion 14.<br \/>\nHow many possible outcomes are there?<br \/>\nAnswer: 8<\/p>\n<p>Explanation:<br \/>\nThe spinner is divided into 8 equal parts<br \/>\nThe number of possible outcomes for the spinner are 8<br \/>\n{ 1,2,3,4,5,6,7,8}<\/p>\n<p>Question 15.<br \/>\nWhat are the favorable outcomes of spinning a number not greater than 3?<br \/>\nAnswer: 3<\/p>\n<p>Explanation:<br \/>\nThere are 3 numbers those are not greater than 3, they are\u00a0 {1,2,3}.<br \/>\nThere are 3 favorable outcomes.<\/p>\n<p>Question 16.<br \/>\nIn how many ways can spinning an even number occur?<br \/>\nAnswer:\u00a0 4<\/p>\n<p>Explanation:<br \/>\nThere are 4 even numbers , they are {2,4,6,8}<br \/>\nSo, there are 4 ways of getting an even number.<\/p>\n<p>Question 17.<br \/>\nIn how many ways can spinning a prime number occur?<\/p>\n<p>Answer:4<\/p>\n<p>Explanation:<br \/>\nThere are 4 prime numbers , they are {2,3,5,7}<br \/>\nSo, there are 4 ways of getting a prime number.<\/p>\n<p><strong>IDENTIFYING OUTCOMES<\/strong> You randomly choose one marble from the bag.(a) Find the number of ways the event can occur. (b) Find the favorable outcomes of the event.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28910\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-13.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 13\" width=\"283\" height=\"258\" \/><\/p>\n<p>There are 9 colored balls in the bag in which ,<br \/>\nThe number of red balls = 3 .<br \/>\nThe number of blue balls = 2<br \/>\nThe number of yellow balls = 1<br \/>\nThe number of purple balls = 2.<br \/>\nThe number of green balls =1<br \/>\nThe number of favorable outcomes = 9.<\/p>\n<p>Question 18.<br \/>\nChoosing blue<br \/>\nAnswer: 2\/9<\/p>\n<p>Explanation :<br \/>\nThe total number of out comes = 9.<br \/>\nThe number of blue balls in the bag = 2<br \/>\nConsider B is the event of getting Blue ball<br \/>\nSo, the probability of getting blue ball, P(B)=\u00a0 (Number of Favorable outcomes) \/ (Total number of outcomes)<br \/>\nP(B) = 2 \/ 9.<br \/>\nTherefore, the probability of getting blue ball is 2\/9 = 0.22.<\/p>\n<p>Question 19.<br \/>\nChoosing green<br \/>\nAnswer: 1\/9<\/p>\n<p>Explanation :<br \/>\nThe total number of out comes = 9.<br \/>\nThe number of green balls in the bag = 1<br \/>\nConsider G is the event of getting Blue ball<br \/>\nSo, the probability of getting green ball, P(G)=\u00a0 (Number of Favorable outcomes) \/ (Total number of outcomes)<br \/>\nP(G) = 2 \/ 9.<br \/>\nTherefore, the probability of getting green ball is 1\/9 = 0.11.<\/p>\n<p><span style=\"font-size: 16px;\">Question 20.<\/span><\/p>\n<p>Choosing purple<\/p>\n<p>Answer: 2\/9<\/p>\n<p>Explanation :<br \/>\nThe total number of out comes = 9.<br \/>\nThe number of purple balls in the bag = 2<br \/>\nConsider P is the event of getting purple ball<br \/>\nSo, the probability of getting purple ball, P(P)=\u00a0 (Number of Favorable outcomes) \/ (Total number of outcomes)<br \/>\nP(P) = 2 \/ 9.<br \/>\nTherefore, the probability of getting purple ball is 2\/9 = 0.22.<\/p>\n<p><span style=\"font-size: 16px;\">Question 21.<\/span><\/p>\n<p>Choosing yellow<\/p>\n<p>Answer: 1\/9<\/p>\n<p>Explanation :<br \/>\nThe total number of out comes = 9.<br \/>\nThe number of yellow balls in the bag = 1<br \/>\nConsider Y is the event of getting yellow ball<br \/>\nSo, the probability of getting yellow ball, P(Y)=\u00a0 (Number of Favorable outcomes) \/ (Total number of outcomes)<br \/>\nP(Y) = 2 \/ 9.<br \/>\nTherefore, the probability of getting yellow ball is 1\/9 = 0.11.<\/p>\n<p><span style=\"font-size: 16px;\">Question 22.<\/span><\/p>\n<p>Choosing not red<br \/>\nAnswer: 0.67<br \/>\nThere are 3 red balls in the bag<br \/>\nThe total number of colored balls in the bag are 9<br \/>\nThe balls other than red balls are 9 &#8211; 3 = 6<br \/>\nTherefore, the probability of getting a ball other than red is<br \/>\nP(E) = Favorable outcomes \/ Total number of outcomes .<br \/>\nWhere, E is the event of getting a ball other than red<br \/>\nP(E) = 6\/9 = 2\/3<br \/>\nTherefore , the probability of choosing not red ball is 2\/3 = 0.67.<\/p>\n<p>Question 23.<br \/>\nChoosing not blue<\/p>\n<p>Answer: 7\/9 = 0.78<\/p>\n<p>Explanation:<br \/>\nThere are 2 blue balls in the bag<br \/>\nThe total number of colored balls in the bag are 9<br \/>\nThe balls other than blue balls are 9 &#8211; 2 = 7<br \/>\nTherefore, the probability of getting a ball other than blue is<br \/>\nP(E) = Favorable outcomes \/ Total number of outcomes .<br \/>\nWhere, E is the event of getting a ball other than blue<br \/>\nP(E) = 7\/9 = 0.78<br \/>\nTherefore , the probability of choosing not blue ball is 7\/9.<\/p>\n<p>Question 24.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the number of ways that choosing not purple can occur. Is your friend correct? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28911\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-14.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 14\" width=\"290\" height=\"111\" \/><\/p>\n<p>Answer: Yes, he is correct<br \/>\nGiven, the number of not purple colors=4<br \/>\nThey are red, blue, green, yellow<br \/>\nTherefore the number of ways that choosing not purple can occur = 4 .<\/p>\n<p><strong>CRITICAL THINKING<\/strong> Tell whether the statement is true or false. If it is false, change the italicized word to make the statement true.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28912\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-15.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 15\" width=\"148\" height=\"311\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-15.png 148w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-15-143x300.png 143w\" sizes=\"(max-width: 148px) 100vw, 148px\" \/><br \/>\nQuestion 25.<br \/>\nSpinning blue and spinning green have the same number of favorable outcomes on Spinner A.<br \/>\nAnswer: False<br \/>\nSpinning blue and spinning Red have the same number of favorable outcomes on spinner A.<\/p>\n<p>Question 26.<br \/>\nThere are three possible outcomes of spinning Spinner A.<br \/>\nAnswer: True<\/p>\n<p>Question 27.<br \/>\nSpinning red can occur in four ways on Spinner B.<br \/>\nAnswer: True<\/p>\n<p>Question 28.<br \/>\nSpinning not green can occur in three ways on Spinner B.<br \/>\nAnswer: False<\/p>\n<p>Spinning not green can occur in four ways on Spinner B.<\/p>\n<p><strong>DESCRIBING LIKELIHOOD<\/strong> Describe the likelihood of the event given its probability.<br \/>\nQuestion 29.<br \/>\nYour soccer team wins \\(\\frac{3}{4}\\) of the time.<br \/>\nAnswer:50<br \/>\nThe likelihood of the event is may or may not happen .<\/p>\n<p>Question 30.<br \/>\nThere is a 0% chance that you will grow12 feet.<br \/>\nAnswer:<br \/>\nThe probability =0<br \/>\nThus, the likelihood of the event is Impossible<br \/>\nTherefore , It is impossible to to grow 12 feet.<\/p>\n<p>Question 31.<br \/>\nThe probability that the sun rises tomorrow is 1.<br \/>\nAnswer:<br \/>\nThe probability 1=100%<br \/>\nThe likelihood of the event is\u00a0 certain<br \/>\nSo, it is sure that the sun rises tomorrow<\/p>\n<p>Question 32.<br \/>\nIt rains on \\(\\frac{1}{5}\\) of the days in June.<br \/>\nAnswer:<br \/>\nThe likelihood of the event is not likely to happen .<\/p>\n<p>Question 33.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou have a 50% chance of being chosen to explain a math problem in front of the class. Describe the likelihood that you are chosen.<br \/>\nAnswer:<br \/>\nGiven,\u00a0 there is 50% chance of being chosen to explain a math problem in front of the class<br \/>\n50% = 0.5<br \/>\nSo, the likelihood of the event is may or may not occur .<br \/>\nthere is 50% chance<\/p>\n<p>Question 34.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou roll a number cube and record the number of times you roll an even number and the number of times you roll an odd number. Describe the likelihood of each event.\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28913\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-16.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 16\" width=\"215\" height=\"81\" \/><br \/>\na. You roll an even number on your next roll.<br \/>\nb. You roll an odd number on your next roll.<br \/>\nAnswer:<\/p>\n<p>a.Explanation:<br \/>\nTotal number times cube rolled = 50<br \/>\nThe frequency for even number =26<br \/>\nConsider E be the event of rolling an even number<br \/>\nP(E)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nP(E)= 26\/50 = 0.72<br \/>\nTherefore , the chances of rolling an even number = 0.72<\/p>\n<p>b.Explanation:<br \/>\nTotal number times cube rolled = 50<br \/>\nThe frequency for odd number =24<br \/>\nConsider O be the event of rolling a odd number<br \/>\nP(O)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nP(O)= 24\/50 = 0.48<br \/>\nTherefore , the chances of rolling a odd number = 0.48<\/p>\n<p>Question 35.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou want to determine whether a coin is fair. You flip the coin and record the number of times you flip heads and the number of times you flip tails.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28914\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-17.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 17\" width=\"186\" height=\"73\" \/><br \/>\na Describe the likelihood that you flip heads on your next flip.<br \/>\nb. Describe the likelihood that you flip tails on your next flip.<br \/>\nc. Do you think the coin is a fair coin? Explain. \u0307\u0307\u0307\u0307\u0307<br \/>\nAnswer:<\/p>\n<p>a.Total number of flips = 25<br \/>\nThe total frequency for heads = 22<br \/>\nNow, the likelihood that you flip heads on your next flip<br \/>\n= Number of heads\/ total<br \/>\n= 22 \/ 25 = 0.88<br \/>\n=88%<br \/>\nThe likelihood of the event is more likely to occur<\/p>\n<p>b.Total number of flips =25<br \/>\nThe total frequency for tails = 3<br \/>\nNow, the likelihood that you flip tails on your next flip<br \/>\n= Number of tails\/ Total<br \/>\n= 3\/25 =0.12<br \/>\nTherefore, the likelihood of the event is not likely to occur<\/p>\n<p>c.Every coin has both sides, { heads, tails}<br \/>\nBut, the probability of tossing coin is not fair<br \/>\nThey do not have 50\/50 outcomes for both heads and tails .<br \/>\nSo the coin is not fair in tossing.<\/p>\n<p>Question 36.<br \/>\n<strong>LOGIC<\/strong><br \/>\nAt a carnival, each guest randomly chooses 1 of 50 rubber ducks and then replaces it. The table shows the numbers of each type of duck that have been drawn so far. Out of 150 draws, how many can you expect to not be a losing duck? Justify your answer.\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307\u0307<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28915\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-18.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 18\" width=\"299\" height=\"133\" \/><\/p>\n<p>Answer:<br \/>\nTotal number of ducks = 25<br \/>\nTotal number of win ducks = 6<br \/>\nNow,<br \/>\nThe probability to expect to not be a losing duck after 105 draws =<br \/>\nwon ducks\/ total =x\/150<br \/>\n6\/25 =x\/150<br \/>\n25x= 900<br \/>\nx= 900\/25<br \/>\nx= 36 =0.36<br \/>\nThe chance to expect to not be a losing duck after 105 draws is &#8216;not likely to occur<\/p>\n<p>Question 37.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nA dodecahedron has twelve sides numbered 1 through 12. Describe the likelihood that each event will occur when you roll the dodecahedron. Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28916\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-19.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 19\" width=\"164\" height=\"148\" \/><br \/>\na. rolling a 1<br \/>\nb. rolling a multiple of 3<br \/>\nc. rolling a number greater than 6<\/p>\n<p>a. rolling a 1<\/p>\n<p>Answer:\u00a0The probability of rolling a 1 is 1\/12<\/p>\n<p>Explanation :<br \/>\nThere are 12 number of outcomes for a dodecahedron,<br \/>\n{1,2,3,4,5,6,7,8,9,10,11,12}<br \/>\nP{O}= favorable outcomes \/ Total number of outcomes.<br \/>\nWhere O is the event of getting number 1<br \/>\np{O}= 1 \/12<br \/>\nTherefore , the probability of rolling 1 is 1\/12.<\/p>\n<p>b. Rolling a multiple of 3<\/p>\n<p>Answer:\u00a0 1\/3<\/p>\n<p>Explanation:<br \/>\nThere are 4 multiples of 3 in a dodecahedron.<br \/>\nThey are, {3,6,9,12}<br \/>\nThere are 12 number of outcomes for a dodecahedron,<br \/>\n{1,2,3,4,5,6,7,8,9,10,11,12}<br \/>\nP{M}= Favorable outcomes\/ Total number of outcomes<br \/>\nWhere, M is the event of rolling a multiple of 3<br \/>\nP{M}= 4\/12 = 1\/3<br \/>\nTherefore, the probability of getting a multiple of 3 is 1\/3<\/p>\n<p>C. Rolling a number greater than 6.<\/p>\n<p>Answer: 1\/2<\/p>\n<p>Explanation:<br \/>\nThere are 6 numbers of which are greater than 6 . they are, {7,8,9,10,11,12}<br \/>\nThere are 12 number of outcomes for a dodecahedron,<br \/>\n{1,2,3,4,5,6,7,8,9,10,11,12}<br \/>\nP{G}= Favorable outcome \/ Total number of outcomes<br \/>\nWhere, G is the event of getting a number greater than 6<br \/>\nP{G} = 6\/12=1\/2<br \/>\nTherefore, the probability of getting a number greater than 6 is 1\/2.<\/p>\n<p>Question 38.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA bargain bin contains classical CDs and rock CDs. There are 60 CDs in the bin. Choosing a rock CD and not choosing a rock CD have the same number of favorable outcomes. How many rock CDs are in the bin?<\/p>\n<p>Answer: 30 Rock CDs<\/p>\n<p>Explanation:<br \/>\nGiven that,<br \/>\nThere are 60 CDs in the bin<br \/>\nSo, There are 60 total number of outcomes<br \/>\nAlso given that, choosing a rock CD and not choosing a rock CD have the same number of favorable outcomes<br \/>\nSo, there is equal probability .<br \/>\nWe can conclude that there are same number of classical CDs and rock CDs<br \/>\nWhich means , 30 +30 = 60<br \/>\nTherefore, there are 30 rock CDs in the bin.<\/p>\n<p>Question 39.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou randomly choose one of the cards and set it aside. Then you randomly choose a second card. Describe how the number of possible outcomes changes after the first card is chosen.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28917\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-20.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 20\" width=\"316\" height=\"203\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-20.png 316w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-20-300x193.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nAnswer:<br \/>\nInitially,<br \/>\nTotal number cards =5<br \/>\nSo, the number of possible outcome =5<br \/>\nIf you choose one card and set it aside , the number of possible outcomes decreases by 1<br \/>\nThen when you randomly choose second card , there are only four cards left<br \/>\nTherefore, the number of possible outcomes decreases by 1 after the first card is chosen.<\/p>\n<p><strong>STRUCTURE<\/strong> A Punnett square is a grid used to show possible gene combinations for the offspring of two parents. In the Punnett square shown, a boy is represented by XY. A girl is represented by XX.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28918\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-7.1-21.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability 7.1 21\" width=\"224\" height=\"165\" \/><br \/>\nQuestion 40.<br \/>\nComplete the Punnett square. Explain why the events \u201chaving a boy\u201d and \u201chaving a girl\u201d are equally likely.<br \/>\nAnswer:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-36804\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-5.jpg\" alt=\"\" width=\"376\" height=\"224\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-5.jpg 376w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-5-300x179.jpg 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<p>There is a chance of 50% female and 50% male<br \/>\nThe probability = 50%<br \/>\nTherefore , the likelihood of the event is equally likely.<\/p>\n<p>Question 41.<br \/>\nTwo parents each have the gene combination Cs. The gene C is for curly hair. The gene s is for straight hair. Any gene combination that includes a C results in curly hair. When all outcomes are equally likely, what is the probability of a child having curly hair?<br \/>\nAnswer: 4<br \/>\nC is considered as X which results for curly hair<br \/>\nsince, there are 4 outcomes includes X<br \/>\nThus, the probability of child having curly hair = 4\/4 =1<br \/>\nTherefore , the probability = 1<br \/>\nSo, the likelihood or the chances of a child having curly hair is certain.<\/p>\n<h3><a id=\"Lesson_7.2_Experimental_and_Theoretical_Probability\"><\/a>Lesson 7.2 Experimental and Theoretical Probability<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Conducting Experiments<br \/>\nWork with a partner. Conduct the following experiments and find the relative frequencies.<br \/>\nExperiment 1<br \/>\n\u2022 Flip a quarter 25 times and record whether each flip lands heads up or tails up.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28919\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-1.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 1\" width=\"270\" height=\"117\" \/><br \/>\nExperiment 2<br \/>\n\u2022 Toss a thumbtack onto a table 25 times and record whether each toss lands point up or on its side.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28920\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-2.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 2\" width=\"496\" height=\"191\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-2.png 496w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-2-300x116.png 300w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><br \/>\na. Combine your results with those of your classmates. Do the relative frequencies change? What do you notice?<br \/>\nb. Everyone in your school conducts each experiment and you combine the results. How do you expect the relative frequencies to change?<br \/>\nc. How many times in 1000 flips do you expect a quarter to land heads up? How many times in 1000 tosses do you expect a thumbtack to land point up? Explain your reasoning.<br \/>\nd. In a uniform probability model, each outcome is equally likely to occur. Can you use a uniform probability model to describe either experiment? Explain.<br \/>\nAnswer:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28921\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-3.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 3\" width=\"187\" height=\"120\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p><strong>The table shows the results of rolling a number cube 50 times. Find the experimental probability of the event.<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28922\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-4.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 4\" width=\"395\" height=\"62\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-4.png 395w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-4-300x47.png 300w\" sizes=\"(max-width: 395px) 100vw, 395px\" \/><br \/>\nQuestion 1.<br \/>\nrolling a 3<br \/>\nAnswer: 8\/50 =\u00a0 0.16<\/p>\n<p>Explanation:<br \/>\nTotal number of trails = 50<br \/>\nFrequency for\u00a0 3 = 8<br \/>\nConsider T be the event of rolling a 3<br \/>\nExperimental probability = P(T)(Number of times an event occurs)\/ (Total number of trails)<br \/>\nP(T)= 8\/50= 0.16<br \/>\nTherefore , the probability of rolling a 3 is 0.16.<\/p>\n<p>Question 2.<br \/>\nrolling an odd number.<br \/>\nAnswer:<br \/>\nThe probability of rolling an odd number = 0.58<\/p>\n<p>Explanation:<br \/>\nTotal number of odd numbers = 3<br \/>\nThey are {1,3,5,}<br \/>\nThe frequency for 1 = 10<br \/>\nThe frequency for 3 =8<br \/>\nThe frequency for 5= 11<br \/>\nTotal frequency = 10 +8+11 = 29<br \/>\nTotal number of trails = 50<br \/>\nConsider O be the event of rolling a Odd number<br \/>\nExperimental probability = P(O)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nP(O)= 29\/50= 0.58<br \/>\nTherefore , the probability of rolling an odd number = 0.58<\/p>\n<p>Question 3.<br \/>\nWhat is the theoretical probability of randomly choosing an X?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28923\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-5.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 5\" width=\"169\" height=\"188\" \/><br \/>\nAnswer: 1\/7 =0.142<\/p>\n<p>Explanation:<br \/>\nNumber of favorable outcomes = 7<br \/>\nConsider X be the event of choosing an X<br \/>\nTheoretical probability P(X)=(Number of favorable outcomes)\/(Total number of outcomes)<br \/>\nP(X)= 1\/7 = 0.142<br \/>\nTherefore, the probability of randomly choosing X =0.142<\/p>\n<p>Question 4.<br \/>\nHow does the experimental probability of rolling a number greater than 1 compare with the theoretical probability?<br \/>\nAnswer:<br \/>\nTheoretical probability\u00a0 is what we expect to happen, where experimental probability\u00a0is what actually happens when we try it out.<br \/>\nThe experimental probability of an event\u00a0cannot be greater than 1\u00a0since the number of trials in which the event can happen cannot be greater than\u00a0the total number of trials.<\/p>\n<p>Question 5.<br \/>\nAn inspector randomly selects 200 pairs of jeans and finds 5 defective pairs. About how many pairs of jeans do you expect to be defective in a shipment of 5000?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28924\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-6.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 6\" width=\"185\" height=\"118\" \/><br \/>\nAnswer: 125 defective jeans<\/p>\n<p>Explanation:<br \/>\nTotal number of pairs = 200<br \/>\nNumber of defective pairs = 5<br \/>\nLet ,x be the number of defective pairs of jeans in a shipment of 5000<br \/>\nNow, the number of defective pair of jeans in a shipment of 5000 =<br \/>\nDefective \/ Total= x\/5000<br \/>\n5\/200 = X\/5000<br \/>\n200 x x =\u00a0 5000 x 5<br \/>\n200x = 25000<br \/>\nx = 25000\/200<br \/>\nx = 125<br \/>\nTherefore there are 125 pairs of jeans are expected\u00a0 to be defective in a shipment of 5000<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 6.<br \/>\nExplain what it means for an event to have a theoretical probability of 0.25 and an experimental probability of 0.3.<br \/>\nAnswer:<br \/>\nIf you have a fair coin, and flip it twice,<br \/>\nThe\u00a0 theoretical probability of getting 2 heads = 0.25<br \/>\nThere&#8217;s 4 outcomes: HH, TT, TH, and HT.<br \/>\n1 out of 4 is 0.25 chance of 2 heads.<br \/>\nBut if you run the experiment and do actual flips, maybe 100 times,<br \/>\nThe average times you get 2 heads might be 0.3 if you got 2 heads 30 times out of a 100.<br \/>\nIt could be just random chance or maybe the coin is slightly heavier on the head side, causing slightly more heads than the theoretical probability.<\/p>\n<p>Question 7.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nYou flip a coin and record the results in the table. Which is different? Find \u201cboth\u201d answers.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28925\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-7.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 7\" width=\"540\" height=\"160\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-7.png 540w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-7-300x89.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><br \/>\nAnswer:<\/p>\n<ol>\n<li>Experimental probability of flipping heads = frequency of heads \/ Total number of trails = 32\/60 =0.53<\/li>\n<\/ol>\n<p>2.\u00a0 \u00a0 \u00a0 \u00a0The fraction of the flips you can expect a result of heads = 32\/60 =0.53<\/p>\n<p>3.\u00a0 \u00a0 \u00a0 \u00a0 The percent of flips result in heads = 0.53 =53%<\/p>\n<p>4.\u00a0 \u00a0 \u00a0 \u00a0 The relative frequency of flipping heads =\u00a0 32\/60 = 0.53<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 8.<br \/>\nContestants randomly draw a ticket from a hat and replace it. The table shows the results after 40 draws. There are 7 winning tickets in the hat. Predict the total number of tickets in the hat. Explain.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28926\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-8.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 8\" width=\"187\" height=\"113\" \/><br \/>\nAnswer:<br \/>\nLet, the total numbers of tickets in the hat = x<br \/>\nGiven that , Number of winning tickets = 7<br \/>\nNumber of winning won after 40 draws = 2<br \/>\nTotal number of tickets =<br \/>\n2\/40 = 7\/x<br \/>\n2x = 280<br \/>\nx = 280\/2<br \/>\nx= 140<br \/>\nTherefore, The total number of tickets in the hat = 140<\/p>\n<p>Question 9.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nYou choose two different songs on a music play list at random. Out of 80 songs on the playlist, 36 are hip hop songs. The first song you choose is a hip hop song. What is the probability that the second song is also a hip hop song? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28927\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-9.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 9\" width=\"192\" height=\"312\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-9.png 192w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-9-185x300.png 185w\" sizes=\"(max-width: 192px) 100vw, 192px\" \/><br \/>\nAnswer:<br \/>\nTotal number of songs = 80<br \/>\nNumber of hip pop songs = 36<br \/>\nGiven that the first song is hip pop<br \/>\nThe probability of playing second song also hip pop =<br \/>\nTotal number of hip pop songs \/ total number of songs<br \/>\nConsider H be the event of playing hip pop<br \/>\nP(H)= 36\/ 80 =0.45<br \/>\nIf there is no repeat :<br \/>\nTotal number of hip pop songs after playing one song = 35<br \/>\nP(H)= 0.43<br \/>\nTherefore ,the likelihood of the event is unlikely to happen.<\/p>\n<h3><a id=\"Experimental_and_Theoretical_Probability_Homework_&amp;_Practice_7.2\"><\/a>Experimental and Theoretical Probability Homework &amp; Practice 7.2<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p><strong>Describe the likelihood of the event given its probability.<\/strong><br \/>\nQuestion 1.<br \/>\nYou randomly guess the correct answer of a multiple choice question \\(\\frac{1}{4}\\) of the time.<br \/>\nAnswer:<br \/>\nThe likelihood of the event is not likely to happen .<\/p>\n<p>Question 2.<br \/>\nThere is a 95% chance that school will not be cancelled tomorrow.<br \/>\nAnswer:<br \/>\nGiven , 95% chance that school will be cancelled tomorrow<br \/>\n95%= 0.95<br \/>\nProbability = 0.95<br \/>\nSo the likelihood of the event is more likely to happen<\/p>\n<p>Find the annual interest rate.<br \/>\nQuestion 3.<br \/>\nI = $16, P = $200, t = 2 years<br \/>\nAnswer: 4%<br \/>\nThe formula for simple interest= Principal x rate x time<br \/>\nI = P x r x t<br \/>\n$16 = $200 x r x 2<br \/>\n$16= 400r<br \/>\nr = 16\/400<br \/>\nr= 0.04<br \/>\n0.04 x 100= 4<br \/>\nTherefore, the annual interest rate = 4%<\/p>\n<p>Question 4.<br \/>\nI = $26.25, P = $500, t = 18 months<br \/>\nAnswer:3.5<br \/>\nThe formula for simple interest= Principal x rate x time<br \/>\nI = P x r x t<br \/>\n$26.25 = $500 x r x 1.5<br \/>\n$26.25= 750r<br \/>\nr = 26.25\/750<br \/>\nr= 0.035<br \/>\n0.035 x 100= 3.5<br \/>\nTherefore, the annual interest rate = 3.5%<\/p>\n<p><strong>Tell whether x and y are proportional.<\/strong><br \/>\nQuestion 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28928\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-10.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 10\" width=\"150\" height=\"67\" \/><br \/>\nAnswer:<br \/>\nThe ratio of x and y for the given values is<br \/>\n1\/8 = 0.12<br \/>\n3\/24= 0.12<br \/>\n9\/75 = 0.12<br \/>\nWe get equal values for all the ratios<br \/>\nTherefore, the relationship given in the table is proportional.<\/p>\n<p>Question 6.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28929\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-11.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 11\" width=\"175\" height=\"70\" \/><br \/>\nAnswer:<br \/>\nThe ratio of x and y for the given values is<br \/>\n0.75\/0.3 =2.5<br \/>\n1.5\/0.6 = 2.5<br \/>\n2.25\/0.9 = 2.5<br \/>\nWe get equal values for all the ratios<br \/>\nTherefore, the relationship given in the table is proportional.<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>CONDUCTING AN EXPERIMENT<\/strong> Use the bar graph below to find the relative frequency of the event. (See Exploration 1, p. 291.)<br \/>\nQuestion 7.<br \/>\nspinning a 6<br \/>\nAnswer: 0.14<\/p>\n<p>Explanation:<br \/>\nTotal number of spins =50<br \/>\nThe number of times 6 spun =7<br \/>\nConsider X be the event of spinning a 6<br \/>\nExperimental probability = P(T)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nP(X)= 7\/50= 0.14<br \/>\nTherefore, the probability spinning a 6= 0.14<\/p>\n<p>Question 8.<br \/>\nspinning an even number<br \/>\nAnswer:0.48<\/p>\n<p>Explanation:<br \/>\nTotal number of spins =50<br \/>\nNumbers of even numbers = 3<br \/>\nThey are {2,4,6}<br \/>\nNumber of times 2 spun = 6<br \/>\nNumber of times 4 spun = 11<br \/>\nNumber of times 6 spun =7<br \/>\nTotal : 24<br \/>\nConsider E be the event of spinning a number less than 3<br \/>\nExperimental probability\u00a0 P(E)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nP(T)= 24\/50=0.48<br \/>\nTherefore the probability of spinning a even number = 0.48<\/p>\n<p><strong>FINDING AN EXPERIMENTAL PROBABILITY<\/strong> Spinning a Spinner .Use the bar graph to \ufb01nd the experimental probability of the event.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28930\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-12.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 12\" width=\"247\" height=\"180\" \/><br \/>\nQuestion 9.<br \/>\nspinning a number less than 3<br \/>\nAnswer:\u00a0 14\/50=0.28<\/p>\n<p>Explanation:<br \/>\nTotal number of spins =50<br \/>\nNumbers less than 3 are {1,2}<br \/>\nNumber of times 1 spun =8<br \/>\nNumber of times 2 spun =6<br \/>\nTotal : 8 +6 = 14<br \/>\nConsider T be the event of spinning a number less than 3<br \/>\nExperimental probability = P(T)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nP(T)= 14\/50=0.28<br \/>\nTherefore, the probability spinning a number less than 3 =0.28<\/p>\n<p>Question 10.<br \/>\nnot spinning a 1<br \/>\nAnswer: 42\/50= 0.84<\/p>\n<p>Explanation:<br \/>\nTotal number of spins =50<br \/>\nThe numbers other than 1 are{2,3,4,5,6}<br \/>\nThe number of times 2 spun = 6<br \/>\nThe number of times 3 spun= 9<br \/>\nThe number of times 4 spun= 11<br \/>\nThe number of times 5 spun= 9<br \/>\nThe number of times 6 spun= 7<br \/>\nTotal : 6+9+11+9+7=42<br \/>\nConsider O be the event of spinning a number less than 3<br \/>\nExperimental probability = P(O)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nP(O)= 42\/ 50= 0.84<br \/>\nTherefore, the probability of spinning a number other than 1 is 0.84.<\/p>\n<p>Question 11.<br \/>\nspinning a 1 or a 3<br \/>\nAnswer:<br \/>\nTotal number of spins =50<br \/>\nNumber of times 1 spun = 8<br \/>\nThe number of times 3 spun= 9<br \/>\nTotal : 8+9 = 17<br \/>\nConsider S be the event spinning a 1 or 3<br \/>\nExperimental probability = P(S)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nP(S)= 17\/ 50= 0.34<br \/>\nTherefore, the probability of spinning a\u00a0 1 OR 3 is 0.34.<\/p>\n<p>Question 12.<br \/>\nspinning a 7<br \/>\nAnswer: 0<\/p>\n<p>Explanation:<br \/>\nThe bar graph consists 6 numbers<br \/>\nThey are, {1,2,3,4,5,6}<br \/>\nSo, it is impossible to spin 7<br \/>\nTherefore the probability of spinning is 0.<\/p>\n<p>Question 13.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend uses the bar graph above to find the experimental probability of spinning. Is your friend correct? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28931\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-13.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 13\" width=\"302\" height=\"115\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-13.png 302w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-13-300x114.png 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><br \/>\nAnswer:<br \/>\nNo, he is wrong<\/p>\n<p>Explanation:<br \/>\nThe formula for finding experimental probability is<br \/>\nExperimental probability P(O)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nConsider O be the event of spinning 4<br \/>\nP(O)=11\/50<br \/>\nTherefore, the experimental probability of spinning a 4 is 0.22<br \/>\nSo, he is wrong<\/p>\n<p>Question 14.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou check 20 laser pointers at random. Three of the laser pointers are defective. What is the experimental probability that a laser pointer is defective?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28933\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-14.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 14\" width=\"341\" height=\"98\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-14.png 341w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-14-300x86.png 300w\" sizes=\"(max-width: 341px) 100vw, 341px\" \/><br \/>\nAnswer: 0.3<br \/>\nExperimental probability = P(T)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nTotal number of lasers = 20<br \/>\nNumber of defective lasers =3<br \/>\nP(T) = 3\/20<br \/>\n= 0.3<br \/>\nTherefore, the experimental probability that a laser pointer is defective is 0.3<\/p>\n<p><strong>FINDING A THEORETICAL PROBABILITY<\/strong> Use the spinner to find the theoretical probability of the event.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28934\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-15.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 15\" width=\"163\" height=\"158\" \/><br \/>\nQuestion 15.<br \/>\nspinning red<br \/>\nAnswer: 0.33<\/p>\n<p>Explanation:<br \/>\nThe spinner is divided into 6 equal parts.<br \/>\nSo, the total number of outcomes of a spinner = 6<br \/>\nIn which 2 parts are red and remaining parts are blue, green , orange and purple<br \/>\nConsider R is the event of getting a red color.<br \/>\nSo, the probability of spinning red color P(R) = ( number of favorable outcomes)\/(Total number of outcomes)<br \/>\nP(R)= 2\/6= 0.33<\/p>\n<p>Question 16.<br \/>\nspinning a 1<br \/>\nAnswer: 1\/6 = 0.16<\/p>\n<p>Explanation:<br \/>\nThe spinner is divided into 6 equal parts.<br \/>\nSo, the total number of outcomes of a spinner = 6<br \/>\n{1,2,3,4,5,6}<br \/>\nConsider ,O is the event of getting 1<br \/>\nSo, the probability of getting 1 is P(O)=( number of favorable outcomes)\/(Total number of outcomes)<br \/>\nP(O)= 1\/6 = 0.16<br \/>\nTherefore the probability of spinning a 1= 0.16<\/p>\n<p>Question 17.<br \/>\nspinning an odd number<br \/>\nAnswer: 3\/6= 0.5<\/p>\n<p>Explanation:<br \/>\nThe number of total outcomes of a spinner = 6<br \/>\nThey are , {1,2,3,4,5,6}<br \/>\nThere are 3 odd numbers, They are {1,3,5}<br \/>\nConsider N is the event of getting an odd number<br \/>\nSo, the probability of spinning an odd number P(N) =( number of favorable outcomes)\/(Total number of outcomes)<br \/>\nP(N)= 3\/6= 0.5.<br \/>\nTherefore, the probability of spinning an odd number = 3\/6 =0.5<\/p>\n<p>Question 18.<br \/>\nspinning a multiple of 2<br \/>\nAnswer: 3\/6= 0.5<\/p>\n<p>Explanation:<br \/>\nThe total number of outcomes of a spinner = 6<br \/>\nThey are , {1,2,3,4,5,6}<br \/>\nThere are 3 multiples of 2 , They are {2,4,6}<br \/>\nConsider M is the event of getting an odd number<br \/>\nSo, the probability of spinning a multiple of 2is\u00a0 P(M) =( number of favorable outcomes)\/(Total number of outcomes)<br \/>\nP(M)= 3\/6= 0.5.<br \/>\nTherefore, the probability of spinning a multiple of 2 = 3\/6 =0.5<\/p>\n<p>Question 19.<br \/>\nspinning a number less than 7<br \/>\nAnswer: 1<\/p>\n<p>Explanation:<br \/>\nThe spinner is divided into 6 equal parts.<br \/>\nSo, the total number of outcomes of a spinner = 6<br \/>\n{1,2,3,4,5,6}<br \/>\nConsider, S is the event of spinning a number less than 7<br \/>\nSo, the probability of spinning a number less than 7 P(S) =( number of favorable outcomes)\/(Total number of outcomes)<br \/>\nP(S)= 6\/6 =1<br \/>\nSo, the probability of spinning a number less than 7 = 1<\/p>\n<p>Question 20.<br \/>\nspinning a 9<br \/>\nAnswer: 0<br \/>\nThe spinner is divided into 6 equal parts numbering from 1 to 6<br \/>\n={1,2,3,4,5,6}<br \/>\nThere is no 9 in the spinner<br \/>\nSo, the probability of spinning 9 is 0<br \/>\nIt is also called as impossible event .<\/p>\n<p>Question 21.<br \/>\n<strong>REASONING<\/strong><br \/>\nEach letter of the alphabet is printed on an index card. What is the theoretical probability of randomly choosing any letter except Z?<br \/>\nAnswer: 25\/26 =0.96<\/p>\n<p>Explanation:<br \/>\nWe know that, there are 26 alphabets.<br \/>\nAlso, the number of \u00a0alphabets other than Z are: 25<br \/>\nLet us consider Z is the event of choosing any letter except Z .<br \/>\nP(Z)= (number of favorable outcomes) \/ (Total number of outcomes )<br \/>\np(Z)= 25\/ 26 =0.96<br \/>\nTherefore, the theoretical probability of choosing a letter except Z is 25\/26 = 0.96<\/p>\n<p><strong>COMPARING PROBABILITIES<\/strong> The bar graph shows the results of spinning the spinner below 200 times. Compare the theoretical and experimental probabilities of the event.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28935\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-16..png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 16.\" width=\"403\" height=\"176\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-16..png 403w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-16.-300x131.png 300w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><br \/>\nQuestion 22.<br \/>\nspinning a 4<br \/>\nAnswer:<br \/>\nTheoretical probability:<br \/>\nTotal number of outcomes = 5<br \/>\nConsider F be the event of spinning 4<br \/>\nTheoretical probability P(F)= (Number of favorable outcome )\/(Total number of outcomes)<br \/>\nP(F)= 1\/5= 0.2<br \/>\nExperimental probability :<br \/>\nTotal number of spins = 200<br \/>\nNumber of times 4 spun =37<br \/>\nConsider F be the event of spinning 4<br \/>\nExperimental probability = P(F)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nP(F)= 37\/200= 0.185<br \/>\nTherefore, the theoretical probability = 0.2<br \/>\nThe experimental probability = 0.18<\/p>\n<p>Question 23.<br \/>\nspinning a 3<br \/>\nAnswer:<br \/>\nTheoretical probability:<br \/>\nTotal number of outcomes = 5<br \/>\nConsider T be the event of spinning 3<br \/>\nTheoretical probability P(T)= (Number of favorable outcome )\/(Total number of outcomes)<br \/>\nP(T)= 1\/5= 0.2<br \/>\nExperimental probability :<br \/>\nTotal number of spins = 200<br \/>\nNumber of times 3 spun = 39<br \/>\nConsider T be the event of spinning 3<br \/>\nExperimental probability = P(T)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nP(T)= 39\/200= 0.195<br \/>\nTherefore, the theoretical probability = 0.16<br \/>\nThe experimental probability = 0.195<\/p>\n<p>Question 24.<br \/>\nspinning a number greater than 4<br \/>\nAnswer:<br \/>\nTheoretical probability:<br \/>\nTotal number of outcomes = 5<br \/>\nConsider N be the event of spinning a number greater than 4<br \/>\nNumbers greater than 4 = {5}<br \/>\nTheoretical probability P(T)= (Number of favorable outcome )\/(Total number of outcomes)<br \/>\nP(T)= 1\/5= 0.2<br \/>\nExperimental probability :<br \/>\nTotal number of spins = 200<br \/>\nConsider N be the event of spinning a number greater than 4<br \/>\nNumber of times 5 spun =40<br \/>\nExperimental probability = P(T)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nP(T)= 40\/200= 0.2<br \/>\nTherefore, the theoretical probability = 0.2<br \/>\nThe experimental probability = 0.2<\/p>\n<p>Question 25.<br \/>\nspinning an odd number<br \/>\nAnswer:<br \/>\nTheoretical probability:<br \/>\nTotal number of outcomes = 5<br \/>\nConsider S be the event of spinning an odd number<br \/>\nTotal odd numbers = 3<br \/>\nThey are {1,3,5}<br \/>\nTheoretical probability P(T)= (Number of favorable outcome )\/(Total number of outcomes)<br \/>\nP(T)= 3\/5= 0.6<br \/>\nExperimental probability :<br \/>\nTotal number of spins = 200<br \/>\nConsider S be the event of spinning an odd number<br \/>\nThe number of time 1 spun=41<br \/>\nThe number of time 3 spun=39<br \/>\nThe number of time 5 spun=40<br \/>\nTotal : 41+39+40= 120<br \/>\nExperimental probability = P(T)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nP(T)= 120\/200= 0.6<br \/>\nTherefore, the theoretical probability = 0.6<br \/>\nThe experimental probability = 0.6<\/p>\n<p>Question 26.<br \/>\n<strong>REASONING<\/strong><br \/>\nShould you use theoretical or experimental probability to predict the number of times you will spin a 3 in 10,000 spins? Explain.<br \/>\nAnswer: theoretical probability<\/p>\n<p>Explanation:<br \/>\nTheoretical probability of event =<br \/>\nTheoretical probability = P(T)=(Number of favorable outcomes)\/ (Total number of outcomes)<br \/>\nNow,<br \/>\nConsider T be the event of spinning 3<br \/>\nP(T)= 1\/6.<\/p>\n<p>Question 27.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA board game uses a bag of 105 lettered tiles. You randomly choose a tile and then return it to the bag. The table shows the number of vowels and the number of consonants after 50 draws. Predict the number of vowels in the bag.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28936\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-16.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 16\" width=\"416\" height=\"131\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-16.png 416w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-16-300x94.png 300w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><br \/>\nAnswer:<br \/>\nlet , X be the number of vowels in the bag.<br \/>\nTotal number of tiles = 105<br \/>\nNumber of vowels after 50 draws = 18<br \/>\nNow, the number of vowels in the bag =<br \/>\nX\/150 = 18\/50<br \/>\n50X=2700<br \/>\nX = 2700\/50<br \/>\nX = 54<br \/>\nTherefore, 54\u00a0 vowels are expected to be in the bag.<\/p>\n<p>Question 28.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nOn a game show, a contestant randomly draws a chip from a bag and replaces it. Each chip says either win or lose. The theoretical probability of drawing a winning chip is \\(\\frac{3}{10}\\). The bag 10contains 9 winning chips.<br \/>\na. How many chips are in the bag?<br \/>\nb. Out of 20 contestants, how many do you expect to draw a winning chip?<br \/>\nAnswer:<br \/>\nGiven , the probability of drawing a winning chip = 3\/10<br \/>\nConsider , x be the number of chips in the bag<br \/>\nThe number of chips = 9<br \/>\nThe ration of strikes in the bag = 9\/x<br \/>\n3\/10 = 9\/x<br \/>\n3x = 90<br \/>\nx= 30<br \/>\nTherefore , there are 30 chips in the bag<\/p>\n<p>Question 29.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThere are 8 females and 10 males in a class.<br \/>\na. What is the theoretical probability that a randomly chosen student is female?<br \/>\nb. One week later, there are 27 students in the class. The theoretical probability that a randomly chosen student is a female is the same as last week. How many males joined the class?<br \/>\nAnswer:<\/p>\n<p>a.Number of females=8<br \/>\nTotal number of students = 8+10= 18<br \/>\nThe theoretical probability that a randomly chosen student is female<br \/>\nConsider F be the event of chosen a female =<br \/>\nP(F)= Number of favorable outcomes \/ Total number of outcomes<br \/>\nP(F)= 8\/18 =0.44<\/p>\n<p>b.Initially,<br \/>\nTotal number of students = 18<br \/>\nIn which , number of females =8<br \/>\nNumber of males =10<br \/>\none week later , the total number of students = 27<br \/>\nGiven, the theoretical probability for choosing girl is same<br \/>\nSo, Number of males joined = 27 -18 = 9<br \/>\nTherefore, 9 males joined<\/p>\n<p>Question 30.<\/p>\n<p><strong>NUMBER SENSE<\/strong><br \/>\nThe table at the right shows the results of flipping two coins 12 times each.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28937\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-17.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 17\" width=\"191\" height=\"68\" \/><br \/>\na. What is the experimental probability of flipping two tails? Using this probability, how many times can you expect to flip two tails in 600 trials?<br \/>\nb. The table at the left shows the results of flipping the same two coins 100 times each. What is the experimental probability of flipping two tails? Using this probability, how many times can you expect to flip two tails in 600 trials?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28938\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-18.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 18\" width=\"194\" height=\"61\" \/><br \/>\nc. Why is it important to use a large number of trials when using experimental probability to predict results?<br \/>\nAnswer:<\/p>\n<p>a.Explanation:<br \/>\nAccording to table,<br \/>\nNumber of turns = 12<br \/>\nFrequency of flipping 2 tails = 1<br \/>\nThe probability of flipping two tails in 600 trails =<br \/>\n1\/12 = x\/600<br \/>\n12x =600<br \/>\nx = 600\/ 12<br \/>\nx = 50<br \/>\nIn 600 trails , flipping 2 tails is expected to be 50 times.<\/p>\n<p>b.Explanation:<br \/>\nAccording to table,<br \/>\nNumber of turns = 100<br \/>\nFrequency of flipping 2 tails = 22<br \/>\nThe probability of flipping two tails in 600 trails =<br \/>\n22\/100= x\/600<br \/>\n100x =13,200<br \/>\nx = 13200\/100<br \/>\nx = 132<br \/>\nIn 600 trails , flipping 2 tails is expected to be 132 times.<\/p>\n<p>c.In\u00a0experimental probability, as the\u00a0number of trials increases, the\u00a0experimental probability\u00a0gets closer to the\u00a0theoretical probability.<br \/>\nSo, it is important to use a large number of trails.<\/p>\n<p>Question 31.<br \/>\n<strong>COMPARING PROBABILITIES<\/strong><br \/>\nThe table shows the possible outcomes of rolling a pair of number cubes. You roll a pair of number cubes 60 times and record your results in the bar graph shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28939\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-19.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 19\" width=\"540\" height=\"199\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-19.png 540w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-19-300x111.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><br \/>\na. Compare the theoretical and experimental probabilities of rolling each sum.<br \/>\nb. Which sum do you expect to be most likely after 500 trials? 1000 trials? Explain your reasoning.<br \/>\nc. Predict the experimental probability of rolling each sum after 10,000 trials. Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>a.<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-39749\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-14.jpg\" alt=\"\" width=\"355\" height=\"220\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-14.jpg 355w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-14-300x186.jpg 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><\/p>\n<p>b. 6 sum is more likely to happen after after 500 trials, 1000 trials, and even after 10,000 trails because the the number of times 6 rolled is greater than other numbers sum.<\/p>\n<p>Question 32.<br \/>\n<strong>PROJECT<\/strong><br \/>\nWhen you toss a paper cup into the air, there are three ways for the cup to land: open-end up, open-end down, or on its side.<br \/>\na. Toss a paper cup 100 times and record your results. Do the outcomes for tossing the cup appear to be equally likely? Explain.<br \/>\nb. Predict the number of times each outcome will occur in 1000 tosses. Explain your reasoning.<br \/>\nc. Suppose you tape a quarter to the bottom of the cup. Do you think the cup will be more likely less likely or to land open-end up? Justify your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28940\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-7.2-20.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability 7.2 20\" width=\"279\" height=\"225\" \/><br \/>\nAnswer:<br \/>\nThe answer will vary<\/p>\n<p>a. The results of tossing a cup 100 times are :<br \/>\nOpen end up\u00a0 \u00a0 \u00a0 = 18<br \/>\nOpen end down = 31<br \/>\nOn its side\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0= 51<br \/>\nThe events of tossing the cup are not equally likely.<\/p>\n<p>b.The probability of the events in 1000 tosses<br \/>\nopen end up =18\/ 100 x 1000 =180<br \/>\nOpen end down = 31\/100 x 1000 =310<br \/>\nOn its side = 51 \/ 100 x1000 =510<\/p>\n<p>c.If you tape quarter to the bottom, it will probably be more likely to land open end up since the weight of the bottom<br \/>\nwill pull the bottom of the cup down and the top of the cap up.<\/p>\n<h3><a id=\"Lesson_7.3_Compound_Events\"><\/a>Lesson 7.3 Compound Events<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Comparing Combination Locks<br \/>\nWork with a partner. You are buying a combination lock. You have three choices.<br \/>\na. One lock has 3 wheels. Each wheel is numbered from 0 to 9. How many possible outcomes are there for each wheel? How many possible combinations are there?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28941\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-1.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 1\" width=\"107\" height=\"223\" \/><br \/>\nb. How can you use the number of possible outcomes on each wheel to determine the number of possible combinations?<br \/>\nc. Another lock has one wheel numbered from 0 to 39. Each combination uses a sequence of three numbers.How many possible combinations are there?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28942\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-2.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 2\" width=\"116\" height=\"166\" \/><br \/>\nd. Another lock has 4 wheels as described. How many possible combinations are there?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28943\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-3.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 3\" width=\"558\" height=\"158\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-3.png 558w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-3-300x85.png 300w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><br \/>\ne. For which lock are you least likely to guess the combination? Why?<br \/>\nAnswer:<\/p>\n<p>The set of all possible outcomes of one or more events is called the sample space. You can use tables and tree diagrams to find the sample space of two or more events.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28944\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-4.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 4\" width=\"187\" height=\"142\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nThe sandwich shop adds a multi-grain bread. Find the sample space. How many sandwiches are possible?<br \/>\nAnswer: sample space = {Sandwich , multi grain bread }<\/p>\n<p>Question 2.<br \/>\nFind the total number of possible outcomes of spinning the spinner and randomly choosing a number from 1 to 5.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28945\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-5.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 5\" width=\"143\" height=\"135\" \/><br \/>\nAnswer:<br \/>\nNumber of colors in the spinner(a) =4<br \/>\nThey are {red, blue, green, yellow}<br \/>\nTotal numbers (b)= 5<br \/>\n{1,2,3,4,5}<br \/>\nTotal number of possible outcomes =<br \/>\nAccording to fundamental principle ,(a x b)=<br \/>\n4 x 5 = 20<br \/>\nTherefore , total number of outcomes = 20<\/p>\n<p>Question 3.<br \/>\nHow many different outfits can you make from 4 T-shirts, 5 pairs of jeans, and 5 pairs of shoes?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28946\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-6.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 6\" width=\"183\" height=\"274\" \/><\/p>\n<p>Answer: 100<\/p>\n<p>Explanation:<br \/>\nNumber of T-shirts(a) = 4<br \/>\nNumber of jeans pairs(b) = 5<br \/>\nNumber of pair of shoes (C)= 5<br \/>\nAccording to fundamental principle,<br \/>\nTotal number of outcomes = a x b x c<br \/>\n=4 x 5 x5<br \/>\n=100<br \/>\nTherefore , about 100 outfits can be made .<\/p>\n<p>Question 4.<br \/>\nIn Example 2, what is the probability of rolling at most 4 and flipping heads?<br \/>\nAnswer:<\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 5.<br \/>\n<strong>FINDING THE SAMPLE SPACE<\/strong><br \/>\nYou randomly choose a flower and ornament for a display case. Find the sample space. How many different displays are possible?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28947\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-7.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 7\" width=\"197\" height=\"198\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-7.png 197w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-7-150x150.png 150w\" sizes=\"(max-width: 197px) 100vw, 197px\" \/><\/p>\n<p>Answer:<br \/>\nTotal number of flowers =3<br \/>\nThey are {daffodil, hyacinth, tulip}<br \/>\nTotal number of ornament =2<br \/>\nThey are {figurine, trophy}<br \/>\nTotal number of outcomes = 3 x 2 = 6<br \/>\nsample space =<br \/>\n{daffodil, figurine} {daffodil, trophy}<br \/>\n{hyacinth, figurine } {hyacinth, trophy }<br \/>\n{tulip, figurine}{tulip, trophy }.<\/p>\n<p>Question 6.<br \/>\n<strong>FINDING THE TOTAL NUMBER OF POSSIBLE OUTCOMES<\/strong><br \/>\nYou randomly choose a number from 1 to 5 and a letter from A to D. Find the total number of possible outcomes.<br \/>\nAnswer: 20<br \/>\nTotal numbers (a) = 5<br \/>\nThey are {1,2,3,4,5}<br \/>\nTotal number of letters (b)=4<br \/>\nThey are {A,B,C,D}<br \/>\nAccording to fundamental theory ,<br \/>\nTotal number of possible outcomes = a x b<br \/>\n= 4 x 5<br \/>\n=20<br \/>\nTherefore , the total number of possible outcomes = 20<\/p>\n<p>Question 7.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nYou roll a number cube and flip a not coin. Which probability does belong with the other three? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28948\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-8.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 8\" width=\"392\" height=\"87\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-8.png 392w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-8-300x67.png 300w\" sizes=\"(max-width: 392px) 100vw, 392px\" \/><br \/>\nAnswer: P(greater than 2 and tails ) probability does not belong with the other three.<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 8.<br \/>\nA tour guide organizes vacation packages at a beach side town. There are 7 hotels, 5 cabins, 4 meal plans, 3 escape rooms, and 2 amusement parks. The tour guide chooses either a hotel or a cabin and then selects one of each of the remaining options. Find the total number of possible vacation packages.<br \/>\nAnswer:<br \/>\nGiven, the tour guide chooses either a hotel or a cabin and then selects one of each of the remaining options.<br \/>\nEvent 1 :<br \/>\nIf the tour guide choose hotel , the total number of possible vacation packages.<br \/>\nAccording to fundamental counting principle ,<br \/>\n7 hotels x 4 meal plans x 3 escape rooms x 2 amusement parks =168<br \/>\nTherefore, The total number of possible vacation packages = 168<br \/>\nEvent 2 :<br \/>\nIf the tour guide choose cabin , the total number of possible vacation packages.<br \/>\nAccording to fundamental counting principle ,<br \/>\n5 cabins x4 meal plans x 3 escape rooms x 2 amusement parks =120<br \/>\nTherefore, The total number of possible vacation packages = 120<\/p>\n<p>Question 9.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA fitness club with 100 members offers one free training session per member in either running, swimming, or weightlifting. Thirty of the fitness center members sign up for the free session. The running and swimming sessions are each twice as popular as the weightlifting session. What is the probability that a randomly chosen fitness club member signs up for a free running session?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28949\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-9.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 9\" width=\"188\" height=\"151\" \/><br \/>\nAnswer:<br \/>\nTotal number of fitness club = 100<br \/>\nThe number of members signed for free up session = 30<br \/>\nGiven , the running and swimming sessions are each twice as popular as the weightlifting session<br \/>\nlet , x be the event of weight lifting and 2x be the event of running and swimming<br \/>\n2x + 2x + x = 30<br \/>\n5x = 30<br \/>\nx = 6<br \/>\nNow,<br \/>\nthe probability that a randomly chosen fitness club member signs up for a free running session=<br \/>\nP(R) =2x \/30<br \/>\n= 2&#215;6\/ 30<br \/>\n= 12\/30<br \/>\nP(R) = 0.4<br \/>\nTherefore , the probability of that a randomly chosen fitness club member signs up for a free running session= 0.4<\/p>\n<h3><a id=\"Compound_Events_Homework_&amp;_Practice_7.3\"><\/a>Compound Events Homework &amp; Practice 7.3<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><\/p>\n<p>Use the bar graph to find the experimental probability of the event.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28950\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-10.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 10\" width=\"225\" height=\"168\" \/><br \/>\nQuestion 1.<br \/>\nrolling a 5<br \/>\nAnswer:<\/p>\n<p>Explanation:<br \/>\nTotal number of spins =100<br \/>\nTotal number of times 5 rolled= 19<br \/>\nConsider T be the event of rolling a 5<br \/>\nExperimental probability = P(T)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nP(T)= 19\/100=0.19<br \/>\nTherefore, the probability of rolling 5 =19\/100=0.19<\/p>\n<p>Question 2.<br \/>\nrolling a 2 or 6<br \/>\nAnswer:<br \/>\nTotal number of spins =100<br \/>\nThe number of times 2 rolled =16<br \/>\nThe probability of rolling 2 = 16 \/100 =0.16<br \/>\nThe number of times 6 rolled = 20<br \/>\nThe probability of rolling 6 = 20\/100 =0.20<\/p>\n<p>Question 3.<br \/>\nrolling at least a 3<br \/>\nAnswer:<\/p>\n<p>Explanation:<br \/>\nThe number of spins = 100<br \/>\nThe number of times 3 =15<br \/>\nConsider S be the event of spinning at least 3 =<br \/>\nP(S) = 15\/100<br \/>\nP(S) = 0.15<\/p>\n<p>Question 4.<br \/>\nrolling a number less than or equal to 4<br \/>\nAnswer: 0.6<\/p>\n<p>Explanation:<br \/>\nTotal number of spins =100<br \/>\nTotal number of times 1 rolled = 12<br \/>\nTotal number of times 2 rolled= 16<br \/>\nTotal number of times 3 rolled = 15<br \/>\nTotal number of times 4 rolled= 17<br \/>\nTotal : 12 + 16 + 15 +17 = 60<br \/>\nConsider L be the event of rolling a number less than or equal to 4<br \/>\nExperimental probability = P(T)=(Number of times an event occurs)\/ (Total number of trails)<br \/>\nP(T)= 60 \/100=0.6<br \/>\nTherefore, the probability of rolling a number less than or equal to 4 = 0.6<\/p>\n<p><strong>Find the product.<\/strong><br \/>\nQuestion 5.<br \/>\n3 . 2<br \/>\nAnswer: 6<\/p>\n<p>Question 6.<br \/>\n5(- 3)<br \/>\nAnswer:<br \/>\n= -12<\/p>\n<p>Question 7.<br \/>\n&#8211; 6(- 2)<br \/>\nAnswer:<br \/>\n= 12<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>COMPARING PASSWORDS<\/strong> Determine which password is less likely to be guessed. (See Exploration 1, p. 299.)<br \/>\nQuestion 8.<br \/>\na password with 3 numbers or a password with 3 capital letters<br \/>\nAnswer: the likelihood of the event is certain to happen with the passwords<\/p>\n<p>Question 9.<br \/>\na password with 6 numbers or a password with 4 capital letters<br \/>\nAnswer: The password with 4 capital letters is more likely to guess than the password with 6 numbers .<\/p>\n<p><strong>USING A TREE DIAGRAM<\/strong> Use a tree diagram to find the sample space and the total number of possible outcomes.<br \/>\nQuestion 10.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28951\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-11.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 11\" width=\"241\" height=\"121\" \/><\/p>\n<p>Answer:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-36841\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-6.jpg\" alt=\"\" width=\"469\" height=\"195\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-6.jpg 1878w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-6-300x125.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-6-1024x426.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-6-768x319.jpg 768w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-6-1536x639.jpg 1536w\" sizes=\"(max-width: 469px) 100vw, 469px\" \/><\/p>\n<p>Total number of possible outcomes = 3x 2 =6<\/p>\n<p>Question 11.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28952\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-12.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 12\" width=\"235\" height=\"98\" \/><br \/>\nAnswer:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-37619\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-13.jpg\" alt=\"\" width=\"512\" height=\"195\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-13.jpg 1489w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-13-300x114.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-13-1024x390.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-13-768x292.jpg 768w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/p>\n<p>Question 12.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28953\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-13.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 13\" width=\"197\" height=\"97\" \/><br \/>\nAnswer:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-37599\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-11.jpg\" alt=\"\" width=\"564\" height=\"262\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-11.jpg 1167w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-11-300x139.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-11-1024x476.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-11-768x357.jpg 768w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 13.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28954\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-14.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 14\" width=\"228\" height=\"95\" \/><br \/>\nAnswer:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-37606\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-12.jpg\" alt=\"\" width=\"586\" height=\"229\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-12.jpg 1474w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-12-300x117.jpg 300w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-12-1024x400.jpg 1024w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-12-768x300.jpg 768w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 14.<br \/>\n<strong>YOU BE THE TEACHER<\/strong><br \/>\nYour friend finds the total number of ways that you can answer a quiz with five true-false questions. Is your friend correct? Explain your reasoning.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28955\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-15.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 15\" width=\"208\" height=\"104\" \/><br \/>\nAnswer: No,<\/p>\n<p>Explanation ,<br \/>\nThe number of outcomes for each question =<br \/>\nPossible answers for question number 1 = 2<br \/>\nPossible answers for question number 2 = 2<br \/>\nPossible answers for question number 3= 2<br \/>\nPossible answers for question number 4= 2<br \/>\nPossible answers for question number 5 = 2<br \/>\nAccording to fundamental counting principle ,<br \/>\nTotal number of outcomes = 2 x 2 x 2 x 2 x 2 = 32<br \/>\nTherefore , You can answer the quiz in 32 different ways<\/p>\n<p><strong>USING THE FUNDAMENTAL COUNTING PRINCIPLE<\/strong> Use the Fundamental Counting Principle to find the total number of possible outcomes.<br \/>\nQuestion 15.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28956\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-16.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 16\" width=\"237\" height=\"88\" \/><br \/>\nAnswer: 12<\/p>\n<p>Explanation:<br \/>\nTotal number of sizes (a) = 3<br \/>\nNumber of flavors (b) = 4<br \/>\nBy using fundamental counting principle ,(a x b)<br \/>\nThe total number of possible outcomes = 3 x 4 = 12<br \/>\nTherefore, total number of outcomes = 12<\/p>\n<p>Question 16.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28957\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-17.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 17\" width=\"260\" height=\"94\" \/><br \/>\nAnswer:20<\/p>\n<p>Explanation:<br \/>\nNumber of batteries (a)= 4<br \/>\nNumber of colors (b)= 5<br \/>\nBy using fundamental counting principle ,( a x b)<br \/>\nThe total number of possible outcomes = 4 x 5 = 20<br \/>\nTherefore, total number of outcomes = 20<\/p>\n<p>Question 17.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28958\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-18.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 18\" width=\"227\" height=\"148\" \/><br \/>\nAnswer:24<\/p>\n<p>Explanation:<br \/>\nNumber of suits (a)= 3<br \/>\nNumber of wigs (b)= 2<br \/>\nNumber of talents (c)= 4<br \/>\nBy using fundamental counting principle ,( a x b x c)<br \/>\nThe total number of possible outcomes = 3 x 2 x 4=24<br \/>\nTherefore, total number of outcomes = 24<\/p>\n<p>Question 18.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28959\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-19.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 19\" width=\"271\" height=\"118\" \/><br \/>\nAnswer:36<\/p>\n<p>Explanation:<br \/>\nNumber of appetizer (a)= 3<br \/>\nNumber of Entre (b)= 4<br \/>\nNumber of dessert (c)= 3<br \/>\nBy using fundamental counting principle ,( a x b x c)<br \/>\nThe total number of possible outcomes = 3 x 4 x 3 = 36<br \/>\nTherefore, total number of outcomes = 36<\/p>\n<p>Question 19.<br \/>\n<strong>CHOOSE TOOLS<\/strong><br \/>\nYou randomly choose one of the marbles. Without replacing the first marble, you choose a second marble.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28960\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-20.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 20\" width=\"162\" height=\"130\" \/><br \/>\na. Name two ways you can find the total number of possible outcomes.<br \/>\nb. Find the total number of possible outcomes.<br \/>\nAnswer:<\/p>\n<p>a. Explanation:<br \/>\nThe tree diagram and fundamental counting principle<\/p>\n<p>b.There are 12 number of possible outcomes<br \/>\nTotal number of balls = 4<br \/>\nTherefore, there are 4 possible outcomes<br \/>\nwithout replacing the first ball, the number of possible outcomes =3<br \/>\nAccording to fundamental principle ,( a x b )<br \/>\n= 4 x 3 = 12<br \/>\nTherefore there are 12 number of outcomes<br \/>\nTree diagram:<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-36736\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-4.jpg\" alt=\"\" width=\"404\" height=\"509\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-4.jpg 547w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-4-238x300.jpg 238w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>FINDING A PROBABILITY<\/strong><br \/>\nYou roll two number cubes. What is the probability of rolling double threes?<br \/>\nAnswer:<br \/>\nNumber of cubes =2<br \/>\n{1,2,3,4,5,6} , {1,2,3,4,5,6}<br \/>\nTotal number of\u00a0 possible outcomes = 6 x 6 = 36<br \/>\nThe probability of rolling double threes =<br \/>\nP(T) = 2\/36 = 0.05<br \/>\nTherefore, the probability of rolling double threes = 0.05<\/p>\n<p><strong>FINDING THE PROBABILITY OF A COMPOUND EVENT<\/strong> You spin the spinner and flip a coin. Find the probability of the compound event.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28961\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-21.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 21\" width=\"153\" height=\"139\" \/><br \/>\nQuestion 21.<br \/>\nspinning a 1 and flipping heads<br \/>\nAnswer: 0.1<\/p>\n<p>Explanation:<br \/>\nThe spinner is divided into 5 equal parts<br \/>\nThey are {12,3,4,5}<br \/>\nTotal number of outcomes =5<br \/>\nConsider O be the event of spinning a 1<br \/>\nP(O)= (Number of favorable outcomes )\/ (Total number of outcomes)<br \/>\nP(O)= 1\/ 5<br \/>\nTotal number of outcomes for a coin =2<br \/>\nThey are {Heads, Tails}<br \/>\nThe probability of flipping a heads<br \/>\nP(H)= 1\/2<br \/>\nThe probability of compound event =<br \/>\n1\/5 x 1\/2 = 1\/10 =0.1<br \/>\nTherefore ,the probability of compound event = 1\/10<\/p>\n<p>Question 22.<br \/>\nspinning an even number and flipping heads<br \/>\nAnswer: 0.2<\/p>\n<p>Explanation:<br \/>\nNumber of even numbers = 2<br \/>\nThey are {2,4}<br \/>\nTotal number of outcomes = 5<br \/>\nConsider E be the event of spinning an even number<br \/>\nP(E) = 2\/5<br \/>\nTotal number of outcomes for a coin =2<br \/>\nThey are {Heads, Tails}<br \/>\nThe probability of flipping a heads<br \/>\nP(H)= 1\/2<br \/>\nThe probability of compound event (a x b)=<br \/>\n2\/5 x 1\/2 = 2\/10 =0.2<br \/>\nTherefore, the probability of compound event = 0.2<\/p>\n<p>Question 23.<br \/>\nspinning a number less than 3 and flipping tails<br \/>\nAnswer: 0.2<\/p>\n<p>Explanation:<br \/>\nTotal number of outcomes = 5<br \/>\nNumber of numbers less than 3 =2<br \/>\nThey are {1,2}<br \/>\nConsider, S be the event of spinning a number less than 3<br \/>\nP(S) = 2\/5<br \/>\nTotal number of outcomes for a coin =2<br \/>\nThey are {Heads, Tails}<br \/>\nThe probability of flipping a heads<br \/>\nP(H)= 1\/2<br \/>\nThe probability of compound event (a x b)=<br \/>\n2\/5 x 1\/2 =2\/10 =0.2<br \/>\nTherefore the probability of compound event = 0.2<\/p>\n<p>Question 24.<br \/>\nspinning a 6 and flipping tails<br \/>\nAnswer: 0<\/p>\n<p>Explanation:<br \/>\nThe spinner is divided into 5 equal parts<br \/>\nThey are {12,3,4,5}<br \/>\nTotal number of outcomes =5<br \/>\nConsider O be the event of spinning a 6<br \/>\nP(O)= (Number of favorable outcomes )\/ (Total number of outcomes)<br \/>\nP(O)= 0<br \/>\nTherefore it is impossible to spin 6<br \/>\nTotal number of outcomes for a coin =2<br \/>\nThey are {Heads, Tails}<br \/>\nThe probability of flipping a tails<br \/>\nP(H)= 1\/2<br \/>\nThe probability of compound event =<br \/>\n0 x 1\/2 =0<br \/>\nTherefore ,the probability of compound event =0<\/p>\n<p>Question 25.<br \/>\nnot spinning a 5 and flipping heads<br \/>\nAnswer:0.4<\/p>\n<p>Explanation:<br \/>\nThe spinner is divided into 5 equal parts<br \/>\nThey are {12,3,4,5}<br \/>\nTotal number of outcomes =5<br \/>\nConsider N be the event of\u00a0 not spinning a 5<br \/>\nFavorable outcomes = 4 .They are {1,2,3,4}<br \/>\nP(N)= (Number of favorable outcomes )\/ (Total number of outcomes)<br \/>\nP(N)= 4\/ 5<br \/>\nTotal number of outcomes for a coin =2<br \/>\nThey are {Heads, Tails}<br \/>\nThe probability of flipping a heads<br \/>\nP(H)= 1\/2<br \/>\nThe probability of compound event =<br \/>\n4\/5 x 1\/2 = 4\/10 =0.4<br \/>\nTherefore ,the probability of compound event = 0.4<\/p>\n<p>Question 26.<br \/>\nspinning a prime number and not flipping heads<br \/>\nAnswer:0.3<\/p>\n<p>Explanation:<br \/>\nTotal number of outcomes = 5<br \/>\nNumber of prime numbers = 3<br \/>\nThey are {2,3,5}<br \/>\nConsider P be the event of spinning a prime number<br \/>\nP(P) = (Number of favorable outcomes )\/ (Total number of outcomes)<br \/>\nP(P) = 3\/5<br \/>\nTotal number of outcomes for a coin =2<br \/>\nThey are {Heads, Tails}<br \/>\nThe probability of not flipping a heads<br \/>\nP(H)= 1\/2<br \/>\nThe probability of compound event =<br \/>\n3\/5 x 1\/2 = 3\/10 =0.3<br \/>\nTherefore ,the probability of compound event = 0.3<\/p>\n<p><strong>FINDING THE PROBABILITY OF A COMPOUND EVENT<\/strong> You spin the spinner, flip a coin, and then spin the spinner again. Find the probability of the compound event.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28962\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-22.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 22\" width=\"139\" height=\"141\" \/><br \/>\nQuestion 27.<br \/>\nspinning blue, flipping heads, then spinning a 1<br \/>\nAnswer:<br \/>\nThe spinner is divided into 3 equal parts<br \/>\nIndicated numerally as {1,2,3} also colored in {red, blue , yellow}<br \/>\nConsider B be the event of spinning blue<br \/>\nP(B) = 1\/3<br \/>\nNumber of outcomes for a coin =2<br \/>\nThey are {Heads , Tails }<br \/>\nConsider H be the event of flipping heads<br \/>\nP(H) = 1\/2<br \/>\nConsider O be the event of spinning 1<br \/>\nP(O)= 1\/3<br \/>\nThe compound probability of compound event =<br \/>\n= 1\/3 x 1\/2 x1\/3<br \/>\n= 1\/18<br \/>\nTherefore , the compound probability of the event is 1\/18.<\/p>\n<p>Question 28.<br \/>\nspinning an odd number, flipping heads, then spinning yellow<br \/>\nAnswer:<br \/>\nThe spinner is divided into 3 equal parts<br \/>\nIndicated numerally as {1,2,3} also colored in {red, blue , yellow}<br \/>\nConsider Y be the event of spinning yellow<br \/>\nP(Y) = 1\/3<br \/>\nNumber of outcomes for a coin =2<br \/>\nThey are {Heads , Tails }<br \/>\nConsider H be the event of flipping heads<br \/>\nP(H) = 1\/2<br \/>\nConsider O be the event of spinning Odd\u00a0 number<br \/>\nNumber of odd numbers = 2<br \/>\nThey are {1,3}<br \/>\nP(O)= 2\/3<br \/>\nThe compound probability of compound event =<br \/>\n= 1\/3 x 1\/2 x2\/3<br \/>\n= 2\/18 =0.11<br \/>\nTherefore , the compound probability of the event is 2\/18.<\/p>\n<p>Question 29.<br \/>\nspinning an even number, flipping tails, then spinning an odd number<br \/>\nAnswer:<br \/>\nThe spinner is divided into 3 equal parts<br \/>\nIndicated numerally as {1,2,3} also colored in {red, blue , yellow}<br \/>\nConsider E be the event of spinning an even number<br \/>\nNumber of even numbers =1<br \/>\nThey are {2}<br \/>\nP(B) = 1\/3<br \/>\nNumber of outcomes for a coin =2<br \/>\nThey are {Heads , Tails }<br \/>\nConsider T be the event of flipping Tails<br \/>\nP(T) = 1\/2<br \/>\nConsider O be the event of spinning an odd number<br \/>\nNumber of odd numbers =2<br \/>\nThey are {1,3}<br \/>\nP(O)= 2\/3<br \/>\nThe compound probability of compound event =<br \/>\n= 1\/3 x 1\/2 x2\/3<br \/>\n= 2\/18 =0.11<br \/>\nTherefore , the compound probability of the event is 2\/18.<\/p>\n<p>Question 30.<br \/>\nnot spinning red, flipping tails, then not spinning an even number<br \/>\nAnswer:<br \/>\nThe spinner is divided into 3 equal parts<br \/>\nIndicated numerally as {1,2,3} also colored in {red, blue , yellow}<br \/>\nConsider R be the event of\u00a0 not spinning red<br \/>\nThe colors other than red are {blue , yellow}<br \/>\nP(R) = 2\/3<br \/>\nNumber of outcomes for a coin =2<br \/>\nThey are {Heads , Tails }<br \/>\nConsider T be the event of flipping tails<br \/>\nP(T) = 1\/2<br \/>\nConsider E be the event of not spinning an even number<br \/>\nnumber of not even numbers =2<br \/>\nThey are {1,3}<br \/>\nP(E)= 2\/3<br \/>\nThe compound probability of compound event =<br \/>\n= 2\/3 x 1\/2 x2\/3<br \/>\n= 4\/18 =0.22<br \/>\nTherefore , the compound probability of the event is 0.22<\/p>\n<p>Question 31.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou randomly guess the answers to two questions on a multiple-choice test. Each question has three choices: A,B, and C.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28963\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-23.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 23\" width=\"213\" height=\"139\" \/><br \/>\na. What is the probability that you guess the correct answers to both questions?<br \/>\nb. Suppose you can eliminate one of the choices for each question. How does this change the probability that both of your guesses are correct?<br \/>\nAnswer:<br \/>\nProbability of an event = Number of favorable outcomes \/ Total number of outcomes<br \/>\nThere is one correct answer for each question.<br \/>\nSo, the number of favorable outcomes = 2<br \/>\nGiven that, there are 3 choices {a, b, c} for each question<br \/>\nSo, total number of outcomes = 6<br \/>\nConsider, C be event that you guess the correct answers to both questions=<br \/>\nP(C)= 2\/6 = 1\/3<br \/>\nTherefore, the probability that you guess the correct answers to both questions =1\/3<\/p>\n<p>b.<br \/>\nAnswer:<br \/>\nThere is a correct answer for each question<br \/>\nSo, the favorable outcomes =2<br \/>\nIf you eliminate one of the choices for each question ,<br \/>\nNow, the choices for the questions are {a, b}<br \/>\nSo, the total number of outcomes =4<br \/>\nConsider, S be the event of choosing correct answer<br \/>\nP(S) = 2\/4<br \/>\n= 0.5<br \/>\nTherefore, the probability of choosing a correct answer is 0.5<\/p>\n<p>Question 32.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou forget the last two digits of your cell phone password.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28964\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-24.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 24\" width=\"129\" height=\"235\" \/><br \/>\na. What is the probability that you randomly choose the correct digits?<br \/>\nb. Suppose you remember that both digits are even. How does this change the probability that you choose the correct digits?<br \/>\nAnswer:<\/p>\n<p>a.Number of digits to be guessed = 2<br \/>\nThere are 10 possible numbers from 0 to 9<br \/>\nBy using fundamental counting principle,<br \/>\nNumber of possible outcomes = 10 x 10 =100<br \/>\nEach digit has one correct answer<br \/>\nSo, the number of favorable outcomes = 2<br \/>\nProbability = Number of favorable outcomes\/ Total number of outcomes<br \/>\nConsider C be the event of choosing correct digits<br \/>\nP(C) = 2\/100 =1\/50<br \/>\nTherefore the probability of choosing correct digits is 1\/50<\/p>\n<p>b.Given that, the two digits to be guessed are even numbers<br \/>\nThe number of even numbers from 0 to 9 = 5<br \/>\nThey are {0,2,4,6,8}<br \/>\nAccording to fundamental counting principle ,<br \/>\nSo, total number of possible outcomes = 5 x 5= 25<br \/>\nEach digit has only one correct answer,<br \/>\nSo number of favorable outcomes = 2<br \/>\nConsider S be the event of choosing correct digits<br \/>\nP(S) = 2\/25 =0.08<br \/>\nTherefore, the probability of choosing correct answer = 0.08<\/p>\n<p>Question 33.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nA combination lock has 3 wheels, each numbered from 0 to 9. You try to guess the combination by writing five different numbers from 0 to 999 on a piece of paper. Find the probability that the correct combination is written on the paper.<br \/>\nAnswer:<br \/>\nThe number of digits numbered from 0 to 9 = 10<br \/>\nYou get to try 5 of the 1000 possible combinations<br \/>\nSo, the probability of getting them all right is 5\/1000 or 1\/200<br \/>\nTherefore ,5 tries, with a 1\/1000 chance each time = 5\/1000 = 1\/200<\/p>\n<p>Question 34.<\/p>\n<p><strong>MODELING REAL LIFE<\/strong><br \/>\nA train has one engine and six train cars. Find the total number of ways an engineer can arrange the train. (The engine must be first.)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28965\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-25.png\" alt=\"Big Ideas Math Answers Grade 7 Chapter 7 Probability 7.3 25\" width=\"571\" height=\"50\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-25.png 571w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Grade-7-Chapter-7-Probability-7.3-25-300x26.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><br \/>\nAnswer:<br \/>\nTotal number of train cars = 6<br \/>\nThe engine must be first So, the total outcomes for train cars<br \/>\nSo , there are 6 possible places for the train cars<br \/>\nNumber of possible outcomes for the first train car = 6<br \/>\nNumber of possible outcomes for the second train car =5<br \/>\nNumber of possible outcomes for the third train car = 4<br \/>\nNumber of possible outcomes for the fourth train car = 3<br \/>\nNumber of possible outcomes for the fifth train car = 2<br \/>\nNumber of possible outcomes for the sixth train car = 1<br \/>\nAccording to fundamental principle ,<br \/>\n6 x 5 x 4 x 3 x 2 x 1 = 720<br \/>\nTherefore, the number of ways you can arrange the train = 720<\/p>\n<p>Question 35.<br \/>\n<strong>REPEATED REASONING<\/strong><br \/>\nYou have been assigned a nine-digit identification number.<br \/>\na. Should you use the Fundamental Counting Principle or a tree diagram to find the total number of possible identification numbers? Explain.<br \/>\nb. How many identification numbers are possible?<br \/>\nc. <strong>RESEARCH<\/strong> Use the Internet to find out why the possible number of Social Security numbers is not the same as your answer to part(b).<br \/>\nAnswer:<\/p>\n<p>a.It is difficult to use tree diagram to find the total number of possible identification numbers because, the total number of identification is very large . So, it is impossible to use tree diagram<br \/>\nTherefore , it is easy to easy to use the fundamental counting principle .<\/p>\n<p>b.Total number of identification digits are from 0 to 9<br \/>\nThey are {0,1,2,3,4,5,6,7,8,9}<br \/>\nThe number of possible numbers from 0 to 9 for first digit = 10<br \/>\nThe number of possible numbers from 0 to 9 for second digit = 10<br \/>\nThe number of possible numbers from 0 to 9 for third\u00a0 digit = 10<br \/>\nThe number of possible numbers from 0 to 9 for fourth digit = 10<br \/>\nThe number of possible numbers from 0 to 9 for fifth digit = 10<br \/>\nThe number of possible numbers from 0 to 9 for sixth digit = 10<br \/>\nThe number of possible numbers from 0 to 9 for seventh digit = 10<br \/>\nThe number of possible numbers from 0 to 9 for eighth digit = 10<br \/>\nThe number of possible numbers from 0 to 9 for ninth digit = 10<br \/>\nAccording to fundamental principle<br \/>\n10x10x10x10x10x10x10x10x10 = 1,000,000,000<br \/>\nTherefore there are 1,000,000,000 possible identification numbers<\/p>\n<p>c.The possible number of Social Security numbers is not the same as your answer to part(b)<br \/>\nBecause , some special numbers are never allocated.<\/p>\n<p>Question 36<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nA social media account password includes a number from 0 to 9, an uppercase letter, a lowercase letter, and a special character, in that order.<br \/>\na. There are 223,080 password combinations. How many special characters are there?<br \/>\nb. What is the probability of guessing the account password if you know the number and uppercase letter, but forget the rest?<br \/>\nAnswer:<\/p>\n<p>a.From 0 to 9, there are a total of 10 values.<br \/>\nFor uppercase letters, there are a total of 26 values from A, B, C, D &#8230;Z<br \/>\nFor lower case letters, there are also a total of 26 values from a, b, c, d &#8230;z.<br \/>\nSo out of these three characters, we have a total of 10 \u00d7 26 \u00d7 26 = 6,760 different combinations.<br \/>\nIf there are 223,080 password combinations<br \/>\nWe need to divide this by 6,760 to calculate the possible values of the special characters.<br \/>\n6,760 \u00d7 Number of possible special characters = 223,080,<br \/>\nNumber of special characters = 223,080 \/ 6760= 33.<br \/>\nSo there are 33 special characters.<br \/>\nIf the number and uppercase values are known then the various lowercase letters and special characters are the unknown values.<br \/>\nThe number of possible combinations = number of lowercase letters \u00d7 number of special characters = 26 \u00d7 33 = 858.<br \/>\nSo the probability of guessing the password is 1 out of 858 combinations.<\/p>\n<p>Question 37.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nFrom a group of 5 scientists, an environmental committee of 3 people is selected. How many different committees are possible?<br \/>\nAnswer:<br \/>\nLet,<br \/>\nThe 5 scientists be indicated as A,B,C,D,E<br \/>\nThe environmental committee of three people =<br \/>\nABC, ABD, ABE ,ACD,ACE , ADE<br \/>\nBCD,BCE, BDE,CDE .<br \/>\nTherefore, there are 10 different ways to form a committee.<\/p>\n<h3><a id=\"Lesson_7.4_Simulations\"><\/a>Lesson 7.4 Simulations<\/h3>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Using a Simulation<br \/>\nWork with a partner. A basketball player makes 80% of her free throw attempts.<br \/>\na. Is she likely to make at least two of her next three free throws? Explain your reasoning.<br \/>\nb. The table shows 30 randomly generated numbers from 0 to 999. Let each number represent three shots. How can you use the digits of these numbers to represent made shots and missed shots?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28966\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-7-Probability-7.4-1.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 7 Probability 7.4 1\" width=\"531\" height=\"418\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-7-Probability-7.4-1.png 531w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-7-Probability-7.4-1-300x236.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><br \/>\nc. Use the table to estimate the probability that of her next three free throws, she makes<\/p>\n<ul>\n<li>exactly two free throws.<\/li>\n<li>at most one free throw.<\/li>\n<li>at least two free throws.<\/li>\n<li>at least two free throws in a row.<\/li>\n<\/ul>\n<p>d. The experiment used in parts (b) and (c) is called a simulation. Another player makes \\(\\frac{3}{5}\\) of her free throws. Describe a simulation that can be 5used to estimate the probability that she makes three of her next four free throws.<br \/>\nAnswer:<br \/>\nA simulation is an experiment that is designed to reproduce the conditions of a situation or process.Simulations allow you to study situations that are impractical to create in real life.<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28967\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-7-Probability-7.4-2.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 7 Probability 7.4 2\" width=\"185\" height=\"67\" \/><\/p>\n<p><strong>Try It<\/strong><\/p>\n<p>Question 1.<br \/>\nYou randomly guess the answers to four true-false questions.<br \/>\na. Design a simulation that you can use to model the answers.<br \/>\nb. Use your simulation to find the experimental probability that you answer all four questions correctly.<\/p>\n<p>Answer:a.\u00a0 There are two answers in a true-false question.<br \/>\nThere is an equal chance of being correct or incorrect.<br \/>\nTherefore, we can use a coin to simulate answers where heads is correct and tails is incorrect.<br \/>\nFlip 4 coins in each trial to simulate the four answers. Run the simulation 50 times.<\/p>\n<p>b.The table below shows the\u00a0 results of simulation 50 times<br \/>\nOut of 50 trails , there are only 4 times all the answers are correct<br \/>\nSo, the probability that you answer all four questions correct =<br \/>\nConsider C be the event of answer all four questions correct<br \/>\nP(C) =4 \/50 = 0.08<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-37108\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-7.jpg\" alt=\"\" width=\"279\" height=\"503\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-7.jpg 421w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-7-166x300.jpg 166w\" sizes=\"(max-width: 279px) 100vw, 279px\" \/>\u00a0 \u00a0<img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-37109\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-8.jpg\" alt=\"\" width=\"288\" height=\"337\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-8.jpg 419w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-8-257x300.jpg 257w\" sizes=\"(max-width: 288px) 100vw, 288px\" \/><\/p>\n<p>Question 2.<br \/>\nA baseball team wins 70% of the time. Design and use a simulation to estimate the probability that the team wins the next three games.<br \/>\nAnswer:<br \/>\nGiven that there is 70% chance of winning<br \/>\nlet us use numbers to determine the win or lose of game<br \/>\nAssume 0-6 numbers to represent win and 7-9 numbers represent lose since, there is 70% chance of winning.<br \/>\nThe table below shows the possible results after simulation 3 numbers 50 times on a random number on a graphing calculator.<br \/>\nOut of 50 trails , 19 of them had three wins<br \/>\nTherefore, the probability = 19\/50 =0.38<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-37111\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-9.jpg\" alt=\"\" width=\"251\" height=\"435\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-9.jpg 443w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-9-173x300.jpg 173w\" sizes=\"(max-width: 251px) 100vw, 251px\" \/><img decoding=\"async\" loading=\"lazy\" class=\"alignnone wp-image-37116\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-10.jpg\" alt=\"\" width=\"251\" height=\"330\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-10.jpg 381w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-10-228x300.jpg 228w\" sizes=\"(max-width: 251px) 100vw, 251px\" \/><\/p>\n<p><strong>Self-Assessment for Concepts &amp; Skills<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 3.<br \/>\n<strong>SIMULATING OUTCOMES<\/strong><br \/>\nFour multiple-choice questions on a quiz each have five answer choices. You randomly guess the answer to each question. Design and use a simulation to find the experimental probability that you answer all of the questions correctly.<br \/>\nAnswer:<br \/>\nGiven , the number of questions = 4<br \/>\nThe number of answer choices for each question = 5<br \/>\nThe experimental probability that you answer all of the questions correctly = 0.5%<\/p>\n<p>Question 4.<br \/>\n<strong>SIMULATING OUTCOMES<\/strong><br \/>\nYou select a marble from a bag and a chip from a box. You have a 20% chance of choosing a green marble and a 90% chance of choosing a red chip. Estimate the probability that you choose a green marble and a red chip.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28968\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-7-Probability-7.4-3.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 7 Probability 7.4 3\" width=\"115\" height=\"83\" \/><br \/>\nAnswer:<br \/>\nGiven ,<br \/>\nThe chance of\u00a0 choosing green marble = 20%<br \/>\nThe chance of choosing a red chip =90%<br \/>\nThe simulation about the probability that you choose green marble and red marble<br \/>\n88 \u00a05 \u00a086 \u00a013 \u00a031 \u00a049 \u00a033 \u00a021 \u00a099 \u00a097<br \/>\n30 \u00a062 \u00a018 \u00a04 \u00a063 \u00a03 \u00a032 \u00a094 \u00a08 \u00a077<br \/>\n24 \u00a087 \u00a074 \u00a056 \u00a019 \u00a042 \u00a061 \u00a075 \u00a081<br \/>\n45 \u00a084 \u00a051 \u00a017 \u00a015 \u00a046 \u00a066 \u00a069 \u00a034 \u00a028<br \/>\n36 \u00a09 \u00a064 \u00a053 \u00a059 \u00a010 \u00a058 \u00a057 \u00a039 \u00a043 \u00a093<br \/>\nThe digits from 1 through 2 in tens place indicate green marble<br \/>\nThe digits from 1 through 9 in tens place indicates red chip<br \/>\nThe experimental probability of choosing green marble and red marble<br \/>\nP(B) = 8\/50 = 0.16<\/p>\n<p><strong>Self-Assessment for Problem Solving<\/strong><br \/>\nSolve each exercise. Then rate your understanding of the success criteria in your journal.<\/p>\n<p>Question 5.<br \/>\nEach day there is a 50% chance that your tablet overheats. Estimate the probability that your tablet overheats on exactly 2 of the next 3 days.<br \/>\nAnswer:<br \/>\nGiven that ,<br \/>\nThe percent of\u00a0 tablet overheats each day = 50%<br \/>\nThe digits from 1 through 5 in the numbers<br \/>\n460 \u00a0677 \u00a0330 \u00a0467 \u00a0654 \u00a0942 \u00a0875 \u00a0217 \u00a0734 \u00a0692<br \/>\n646 \u00a0421 \u00a0222 \u00a0804 \u00a0399 \u00a0380 \u00a0103 \u00a0977 \u00a0991 \u00a0996<br \/>\n367 \u00a0337 \u00a0760 \u00a0495 \u00a0280 \u00a0359 \u00a0726 \u00a0349 \u00a0605 \u00a0649<br \/>\n573 \u00a0836 \u00a0413 \u00a0196 \u00a0475 \u00a0470 \u00a0315 \u00a0911 \u00a0122 \u00a0970<br \/>\n369 \u00a0666 \u00a0908 \u00a0431 \u00a0396 \u00a0230 \u00a0885 \u00a0863 \u00a0333 \u00a0762<br \/>\nThe digits 1 through 5 at least two in a three digit number indicate that your tablet overheats on exactly 2 of the next 3 days.<br \/>\nThe experimental probability that your tablet overheats on exactly 2 of the next 3 days<br \/>\nP(S) = 15\/ 50 = 0.3<\/p>\n<p>Question 6.<br \/>\n<strong>DIG DEEPER<\/strong><br \/>\nThe probability that a homeowner needs a plumber this year is 22%. The probability that the homeowner needs a septic tank specialist is 14%. Estimate the probability that the homeowner needs a plumber, but not a septic tank specialist.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28969\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-7-Probability-7.4-4.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 7 Probability 7.4 4\" width=\"173\" height=\"119\" \/><br \/>\nAnswer:<br \/>\nGiven that,<br \/>\nThe probability home owner needs a plumber this year = 22%<br \/>\nThe probability that home owner needs septic tank specialist = 14%<br \/>\nThe probability that the home owner needs plumber but not septic tank specialist<br \/>\n80 \u00a052 \u00a096 \u00a094 \u00a077 \u00a049 \u00a074 \u00a016 \u00a079 \u00a068<br \/>\n45 \u00a098 \u00a034 \u00a047 \u00a048 \u00a057 \u00a012 \u00a062 \u00a021 \u00a071<br \/>\n60 \u00a082 \u00a078 \u00a011 \u00a064 \u00a028 \u00a043 \u00a022 \u00a075 \u00a019<br \/>\n76 \u00a065 \u00a017 \u00a081 \u00a087 \u00a014 \u00a038 \u00a027 \u00a06 \u00a042<br \/>\n37 \u00a040 \u00a051 \u00a015 \u00a02 \u00a013 \u00a092 \u00a090 \u00a073 \u00a07<br \/>\nThe numbers 1 through 2 in tens place indicates owner needs plumber<br \/>\nThe number 2 through 9 in once place\u00a0 indicate owner does not needs tank specialist<br \/>\nP(S) = 11 \/ 50 = 0.22<\/p>\n<h3><a id=\"Simulations_Homework_&amp;_Practice_7.4\"><\/a>Simulations Homework &amp; Practice 7.4<\/h3>\n<p><strong>Review &amp; Refresh<\/strong><br \/>\nYou flip a coin and roll the 20-sided figure. Find the probability of the compound event.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28970\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-7-Probability-7.4-5.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 7 Probability 7.4 5\" width=\"130\" height=\"128\" \/><br \/>\nQuestion 1.<br \/>\nFlipping tails and rolling at least a 14<br \/>\nAnswer:<br \/>\nThe total numbers of outcomes for a coin = 2<br \/>\nThey are {Tails, heads }<br \/>\nConsider T be the event of flipping tails<br \/>\nP(T) = 1\/2<br \/>\nThe number of outcomes for a 20 sided figure\u00a0 = 20<br \/>\nThe probability of rolling at least a 14<br \/>\nConsider F be the event of rolling at least a 14<br \/>\nP(F) = 1\/ 20<br \/>\nCompound event ( a x b )<br \/>\n= 1\/2 x 1\/20 = 1\/40<\/p>\n<p>Question 2.<br \/>\nFlipping heads and rolling less than 3<br \/>\nAnswer:<br \/>\nThe total numbers of outcomes for a coin = 2<br \/>\nThey are {Tails, heads }<br \/>\nConsider H be the event of flipping heads<br \/>\nP(H ) = 1\/2<br \/>\nThe number of outcomes for a 20 sided figure\u00a0 = 20<br \/>\nConsider L be the event of rolling less than 3<br \/>\nNumber of numbers less than 3 = 2<br \/>\nThey are {1,2}<br \/>\nP(L) = 2\/ 20 = 1\/10<br \/>\nCompound event ( a x b )<br \/>\n= 1\/2 x 1\/10 = 1\/20<\/p>\n<p>Simplify the expression.<br \/>\nQuestion 3.<br \/>\n5(a &#8211; 2)<br \/>\nAnswer:<br \/>\n5(a &#8211; 2) =0<br \/>\n5a -10 =0<br \/>\n5a =10<br \/>\na=10\/5<br \/>\na =2<\/p>\n<p>Question 4.<br \/>\n&#8211; 7(1 + 3x)<br \/>\nAnswer:<br \/>\n&#8211; 7(1 + 3x) =0<\/p>\n<p>-7 &#8211; 21x=0<br \/>\n-21x= 7<br \/>\nx= 7\/-21<br \/>\nx = -0.33<\/p>\n<p>Question 5.<br \/>\n&#8211; 1(3p &#8211; 8)<br \/>\nAnswer:<br \/>\n&#8211; 1(3p &#8211; 8) =0<br \/>\n-3p +8 =0<br \/>\np =-8\/-3\u00a0 =-2.6<\/p>\n<p><strong>Concepts, Skills, &amp; Problem Solving<\/strong><\/p>\n<p><strong>USING A SIMULATION<\/strong> A medicine is effective for 80% of patients. The table shows 30 randomly generated numbers from 0 to 999. Use the table to estimate the probability of the event. (See Exploration 1, p. 307.)<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28971\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-7-Probability-7.4-6.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 7 Probability 7.4 6\" width=\"258\" height=\"198\" \/><br \/>\nQuestion 6.<br \/>\nThe medicine is effective on each of three patients.<br \/>\nAnswer:<br \/>\nLet the, digits 1 through 8 in the tens place represent the medicine is effective<br \/>\nP(E) = 24\/30<\/p>\n<p>Question 7.<br \/>\nThe medicine is effective on fewer than two of the next three patients.<br \/>\nAnswer:<br \/>\nP(N) = 6\/30 = 0.2<\/p>\n<p><strong>SIMULATING OUTCOMES<\/strong> Design and use a simulation to find the experimental probability.<br \/>\nQuestion 8.<br \/>\nIn your indoor garden, 50% of seeds sprout. What is the experimental probability that at least one of your next three seeds sprouts?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28972\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-7-Probability-7.4-7.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 7 Probability 7.4 7\" width=\"214\" height=\"140\" \/><br \/>\nAnswer:<br \/>\nUse the random number generator on a graphing calculator.<br \/>\nRandomly generate 50 numbers from 0 to 99. The table below shows the results.<br \/>\nLet the digits 1 through 5 in the tens place represent the seeds are sprout<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-39985\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-15.jpg\" alt=\"\" width=\"497\" height=\"115\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-15.jpg 497w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Book-7th-Grade-Answer-Key-probability-Image-15-300x69.jpg 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><\/p>\n<p>P(rain both days) =6\/50<br \/>\nThe experimental probability is 6\/50 = 0.12, or 12%.<\/p>\n<p>Question 9.<br \/>\nAn archer hits a target 50% of the time. What is the experimental probability that the archer hits the target exactly four of the next five times?<br \/>\nAnswer:<br \/>\nGiven , the archer hits the target = 50%<br \/>\n25 \u00a082 \u00a053 \u00a049 \u00a024 \u00a095 \u00a031 \u00a066\u00a0 40 \u00a090<br \/>\n42 \u00a030 \u00a09 \u00a078 \u00a04 \u00a080 \u00a016 \u00a099 \u00a023 \u00a085 \u00a039<br \/>\n44 \u00a06 \u00a061 \u00a046 \u00a05 \u00a087 \u00a064 \u00a036 \u00a021 \u00a057 \u00a058<br \/>\n98 \u00a081 \u00a013 \u00a097 \u00a029 \u00a018 \u00a092 \u00a022 \u00a077 \u00a035<br \/>\n55 \u00a014 \u00a060 \u00a028 \u00a038 \u00a089 \u00a056 \u00a069<br \/>\nBecause, the makes 50 % of shots 1 to 50 represents successful shots .<br \/>\nthe experimental probability that the archer hits the target exactly four of the next five times<br \/>\nP(X) = 25\/50 =0.5 = 50%.<\/p>\n<p>Question 10.<br \/>\nA bank randomly selects one of four free gifts to send to each new customer. Gifts include a calculator, a key chain, a notepad, and a pen. What is the experimental probability that the next two new customers both receive calculators? that neither receives a calculator?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28973\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-7-Probability-7.4-8.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 7 Probability 7.4 8\" width=\"106\" height=\"152\" \/><br \/>\nAnswer:<br \/>\nGiven that ,<br \/>\nGifts include a calculator, a key chain, a notepad, and a pen.<br \/>\nThe experimental probability that the next two new customers both receive calculators=<br \/>\nP(C) =1\/4 x1\/4 = 1\/16<br \/>\nThe experimental probability that the next two new customers both neither receive calculators=<br \/>\nP(N) = 3\/4 x 3\/4 = 9\/16<\/p>\n<p>Question 11.<br \/>\nEmployees spin a reward wheel. The wheel is equally likely to stop on each of six rewards labeled A\u2013F. What is the experimental probability that fewer than two of the next three spins land on reward A?<br \/>\nAnswer:<br \/>\nGiven , The six rewards are labelled as {A,B,C,D,E,F}<br \/>\nWhat is the experimental probability that fewer than two of the next three spins land on reward A<br \/>\n92 \u00a072 \u00a041 \u00a033 \u00a083 \u00a04 \u00a060 \u00a032 \u00a06 \u00a081<br \/>\n1 \u00a012 \u00a061 \u00a057 \u00a093 \u00a027 \u00a046 \u00a029 \u00a042\u00a0 47<br \/>\n21 \u00a079 \u00a023 \u00a045 \u00a016 \u00a063 \u00a026 \u00a087 \u00a014 \u00a068<br \/>\n75 \u00a038 \u00a094\u00a0 24\u00a0 20 \u00a086 \u00a082 \u00a070 \u00a08 \u00a097<br \/>\n39 \u00a059 \u00a019 \u00a064 \u00a055 \u00a025 \u00a077 \u00a09 \u00a088 \u00a037<br \/>\nthe experimental probability that fewer than two of the next three spins land on reward A = 4\/50<\/p>\n<p><strong>USING NUMBER CUBES<\/strong> Design and use a simulation with number cubes to estimate the probability.<br \/>\nQuestion 12.<br \/>\nYour lawnmower does not start on the first try \\(\\frac{1}{6}\\) of the time. Estimate the probability that your lawnmower will not start on the first try exactly one of the next two times you move the lawn.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28974\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-7-Probability-7.4-9.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 7 Probability 7.4 9\" width=\"205\" height=\"191\" \/><br \/>\nAnswer:<br \/>\nGiven the probability of the event is 1\/6 = 16<br \/>\nThe simulation of random generate calculator about 50 numbers<br \/>\nThe digits from 1 through 16 indicates the event<br \/>\n50 \u00a099 \u00a088 \u00a06 \u00a098 \u00a076 \u00a063 \u00a021 \u00a065 \u00a042<br \/>\n96 \u00a084 \u00a092 \u00a037 \u00a027 \u00a033 \u00a011 \u00a057 \u00a069 \u00a068<br \/>\n48 \u00a040 \u00a010 \u00a030 \u00a024 \u00a026 \u00a067 \u00a047 \u00a060 \u00a034<br \/>\n59 \u00a087 \u00a018 \u00a078 \u00a07 \u00a079 \u00a012 \u00a095 \u00a09 \u00a08 \u00a01<br \/>\n86 \u00a038 \u00a045 \u00a093 \u00a044 \u00a04 \u00a015 \u00a073 \u00a039<br \/>\nThe experimental probability of the event is 10\/50<br \/>\nP(S) = 0.2<\/p>\n<p>Question 13.<br \/>\nAn application on your phone correctly identifies four out of every six songs. Estimate the probability that at least three of the next four songs are correctly identified.<br \/>\nAnswer:<\/p>\n<p><strong>SIMULATING OUTCOMES<\/strong> Design and use a simulation to find the experimental probability.<br \/>\nQuestion 14.<br \/>\nTwo beakers are used in a lab test. What is the experimental probability that there are reactions in both beakers during the lab test?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28975\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-7-Probability-7.4-10.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 7 Probability 7.4 10\" width=\"203\" height=\"81\" \/><br \/>\nAnswer:<br \/>\nThe simulation of beaker 1 and beaker 2 have reactions<br \/>\nThe digits 1 through 8 in tens place indicate probability of beaker 1<br \/>\nThe digits 1 through 5 in once place indicate probability of beaker 2<br \/>\n52 66 73 68 75 28 35 47 48 2<br \/>\n16 68 49 3 77 35 92 78 6 6<br \/>\n58 18 89 39 24 80 32 41 77 21<br \/>\n32 40 96 59 86 1 12 0 94 73<br \/>\n40 71 28 61 1 24 37 25 3 25<br \/>\nThe experimental probability that there are reactions in both beakers during the lab test<br \/>\nP(R) =32\/50 = 0.64<\/p>\n<p>Question 15.<br \/>\nYou use a stain remover on two separate stains on a shirt. What is the experimental probability that the stain remover removes both the mud stain and the food stain?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28976\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-7-Probability-7.4-11.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 7 Probability 7.4 11\" width=\"219\" height=\"79\" \/><br \/>\nAnswer:<br \/>\nThe simulation of random generator calculator is as follows:<br \/>\nThe digits 1 through 9 in tens place indicate the event in mud<br \/>\nThe digits 1 through 8 in once place indicate the event of stain removal in food<br \/>\n62 \u00a035 \u00a050 \u00a043 \u00a096 \u00a037 \u00a070 \u00a031 \u00a059 \u00a040<br \/>\n55 \u00a092 \u00a089 \u00a014 \u00a010 \u00a041 \u00a087 \u00a095 \u00a011 \u00a099<br \/>\n12 \u00a053 \u00a071 \u00a026 \u00a038 \u00a024 \u00a080 \u00a036 \u00a016 \u00a042<br \/>\n85 \u00a032 \u00a03 \u00a033 \u00a047 \u00a01 \u00a049 \u00a051 \u00a08 \u00a023 \u00a088<br \/>\n69 \u00a015 \u00a064 \u00a084 \u00a081 \u00a060 \u00a066 \u00a072 \u00a074<br \/>\nThe experimental probability that the stain remover removes both the mud stain and the food stain<br \/>\nP(S) = 41\/50 = 0.82<\/p>\n<p>Question 16.<br \/>\n<strong>DIG DEEPER!<\/strong><br \/>\nThe probability that a computer crashes one or more times in a month is 10%. Estimate the probability that the computer crashes at least one or more times per month for two months in a row during the first half of the year.<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<strong>MODELING REAL LIFE<\/strong><br \/>\nYou visit an orchard. The probability that you randomly select a ripe apple is 92%. The probability that you randomly select a ripe cherry is 86%. Estimate the probability that you pick an apple that is ripe and a cherry that is not ripe.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28977\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Solutions-Grade-7-Chapter-7-Probability-7.4-12.png\" alt=\"Big Ideas Math Solutions Grade 7 Chapter 7 Probability 7.4 12\" width=\"198\" height=\"134\" \/><br \/>\nAnswer:<br \/>\nGiven , the probability that you randomly select a ripe apple = 92%<br \/>\nThe probability\u00a0 that you pick a ripe cherry = 86%<br \/>\nThe digits from 1 through 8 in tens place indicates event of choosing a ripe apple<br \/>\nThe digits 9\u00a0 in once place indicates event of not choosing a ripe cherry<br \/>\n75 \u00a099 \u00a069 \u00a033 \u00a067 \u00a01 \u00a022 \u00a017 \u00a018 \u00a037<br \/>\n29\u00a0 27 \u00a09 \u00a012 \u00a054 \u00a07 \u00a031 \u00a039 \u00a026 \u00a087<br \/>\n10 \u00a072 \u00a082 \u00a042 \u00a036 \u00a085 \u00a074 \u00a03 \u00a05 \u00a092<br \/>\n29\u00a0 11 \u00a021 \u00a081 \u00a076 \u00a077 \u00a052 \u00a013 \u00a090<br \/>\n15 \u00a073 \u00a069\u00a0 70 \u00a08 \u00a023 \u00a053 \u00a059 \u00a051 \u00a044 \u00a048<br \/>\nThe probability that you pick an apple that is ripe and a cherry that is not ripe = 9\/50<\/p>\n<p>Question 18<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nYou use a simulation to find an experimental probability. How does the experimental probability compare to the theoretical probability as the number of trials increases?<br \/>\nAnswer:<br \/>\nExperimental probability\u00a0is the result of an\u00a0experiment.\u00a0Theoretical probability\u00a0is what is expected to happen.<br \/>\nIn\u00a0experimental probability, as the number of trials increases, the\u00a0experimental probability\u00a0gets closer to the theoretical\u00a0probability.<\/p>\n<p>Question 19.<br \/>\n<strong>LOGIC<\/strong><br \/>\nAt a restaurant,30% of customers donate to charity in exchange for a coupon. Estimate the probability that it will take at least four customers to find one who donates.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Probability_Connecting_Concepts\"><\/a>Probability Connecting Concepts<\/h3>\n<p><strong>Using the Problem-Solving Plan<\/strong><br \/>\nQuestion 1.<br \/>\nIn an Internet contest, gift cards and bicycles are given as prizes in the ratio 9 : 1. Estimate the probability that at least two of three randomly selected winners receive bicycles.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28979\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cc-1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability cc 1\" width=\"180\" height=\"171\" \/><br \/>\nUnderstand the problem.<br \/>\nYou know the ratio of gift cards to bicycles awarded in the contest. You want to find the probability that atleast two of three randomly selected winners receive bicycles.<br \/>\nMake a plan.<br \/>\nUse the ratio to find the theoretical probability that a randomly selected winner receives a bicycle. Then use a simulation involving 50 randomly generated three-digit numbers to estimate the probability that at least two of three randomly selected winners receive bicycles.<br \/>\nSolve and check.<br \/>\nUse the plan to solve the problem. Then check your solution.<\/p>\n<p>Answer:<\/p>\n<p>Question 2.<br \/>\nA board game uses the spinner shown.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28980\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cc-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability cc 2\" width=\"589\" height=\"150\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cc-2.png 589w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cc-2-300x76.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><br \/>\na. Use theoretical probability to predict the number of times you will spin a number greater than or equal to 8 in 30 spins.<br \/>\nb. You play the game and record the results of 30 spins. Find the percent error of your prediction in part(a).<br \/>\nAnswer:<br \/>\na. Theoretical probability = number of favorable\/ outcomes by total number of outcomes<br \/>\nTotal number of outcomes = 10<br \/>\nThe probability of spinning a number greater than or equal to 8 P(S) = 3\/8 = 0.375<br \/>\nb. The experimental probability =<br \/>\nP(S) = 12\/30= 0.4<\/p>\n<p>Question 3.<br \/>\nThe tiles shown are placed in a bag. You randomly select one of the tiles, return it to the bag, and then randomly select another tile. What is the probability that the product of the numbers on the tiles selected is greater than zero? Justify your answer.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28981\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cc-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability cc 3\" width=\"103\" height=\"88\" \/><br \/>\nAnswer:<br \/>\nTotal number of tiles = 5<br \/>\n= 5&#215;5 = 25 total number of outcomes<br \/>\nThe probability that the product of the numbers on the tiles selected is greater than zero<br \/>\nP(Z) = 2\/ 25<br \/>\nThey are {1 x 2= 2 } and {2x 1 = 2 }<br \/>\nTherefore the probability of the product of the numbers on the tiles selected is greater than zero = 2\/25 = 0.08<\/p>\n<p><strong>Performance Task<\/strong><\/p>\n<p>Fair and Unfair Carnival Games<br \/>\nAt the beginning of this chapter, you watched a STEAM Video called \u201cMassively Multi player Rock Paper Scissors.\u201d You are now ready to complete the performance task related to this video, available at BigIdeasMath.com. Be sure to use the problem-solving plan as you work through the performance task.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28982\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cc-4.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability cc 4\" width=\"350\" height=\"177\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cc-4.png 350w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cc-4-300x152.png 300w\" sizes=\"(max-width: 350px) 100vw, 350px\" \/><\/p>\n<h3><a id=\"Probability_Chapter_Review\"><\/a>Probability Chapter Review<\/h3>\n<p><strong>Review Vocabulary<\/strong><\/p>\n<p>Write the definition and give an example of each vocabulary term.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28983\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-1.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability cr 1\" width=\"559\" height=\"101\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-1.png 559w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-1-300x54.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p><strong>Graphic Organizers<\/strong><\/p>\n<p>You can use a Four Square to organize information about a concept. Each of the four squares can be a category, such as definition, vocabulary, example, non-example, words, algebra, table, numbers, visual, graph,or equation. Here is an example of a Four Square for probability.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28984\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-2.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability cr 2\" width=\"529\" height=\"296\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-2.png 529w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-2-300x168.png 300w\" sizes=\"(max-width: 529px) 100vw, 529px\" \/><br \/>\nChoose and complete a graphic organizer to help you study the concept.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28985\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-3.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability cr 3\" width=\"287\" height=\"285\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-3.png 287w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-3-150x150.png 150w\" sizes=\"(max-width: 287px) 100vw, 287px\" \/><br \/>\n1. favorable outcomes<br \/>\n2. relative frequency<br \/>\n3. experimental probability<br \/>\n4. theoretical probability<br \/>\n5. Fundamental Counting Principle<br \/>\n6. compound event<br \/>\n7. simulation<\/p>\n<p><strong>Chapter Self-Assessment<\/strong><\/p>\n<p>As you complete the exercises, use the scale below to rate your understanding of the success criteria in your journal.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28986\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-4.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability cr 4\" width=\"588\" height=\"79\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-4.png 588w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-4-300x40.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p><strong>7.1 Probability (pp. 283\u2013290)<\/strong><br \/>\nLearning Target: Understand how the probability of an event indicates its likelihood.<\/p>\n<p>You randomly choose one toy race car.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28987\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-5.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability cr 5\" width=\"266\" height=\"155\" \/><br \/>\nQuestion 1.<br \/>\nHow many possible outcomes are there?<br \/>\nAnswer:<br \/>\nThere are 5 green cars , one blue car and one red car<br \/>\nSo the possible outcomes are 7<br \/>\nThey are {green , red, blue}<\/p>\n<p>Question 2.<br \/>\nWhat are the favorable outcomes of choosing a car that is not green?<br \/>\nAnswer: 2<br \/>\nNumber of green cars = 5<br \/>\nNumber of cars that is not green = 2<br \/>\nThey are {blue , red}<br \/>\nTherefore the possible outcomes of choosing a car that is not green = 2<\/p>\n<p>Question 3.<br \/>\nIn how many ways can choosing a green car occur?<br \/>\nAnswer: 5<br \/>\nNumber of green cars = 5<br \/>\nSo, choosing a green car can occur in 5 ways<br \/>\nYou spin the spinner. (a) Find the number of ways the event can occur. (b) Find the favorable outcomes of the event.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28988\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-6.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability cr 6\" width=\"169\" height=\"162\" \/><br \/>\nQuestion 4.<br \/>\nspinning a 1<br \/>\nAnswer:<br \/>\nThe spinner is divided into 8 equal parts<br \/>\nnumbered with two 1s , three 2s and three 3s<br \/>\n{1,1,2,2,2,3,3,3}<br \/>\nThe number of favorable outcomes of spinning a 1 = 2<br \/>\nTotal number of outcomes = 8<br \/>\nConsider O be the event of spinning a 1<br \/>\nProbability P(O) = Number of favorable outcomes\/ Total number of outcomes<br \/>\nP(O) = 2\/8 =1\/4<br \/>\nSo, the probability of spinning a 1 is 0.25<\/p>\n<p>Question 5.<br \/>\nspinning a 3<br \/>\nAnswer:<br \/>\nThe spinner is divided into 8 equal parts<br \/>\nnumbered with two 1s , three 2s and three 3s<br \/>\n{1,1,2,2,2,3,3,3}<br \/>\nThe number of favorable outcomes of spinning a 3 = 3<br \/>\nTotal number of outcomes = 8<br \/>\nConsider T be the event of spinning a 3<br \/>\nProbability P(T) = Number of favorable outcomes\/ Total number of outcomes<br \/>\nP(T) = 3\/8 = 0.37<br \/>\nTherefore, the probability of spinning a 3 = 0.37<\/p>\n<p>Question 6.<br \/>\nspinning an odd number<br \/>\nAnswer:<br \/>\nThe spinner is divided into 8 equal parts<br \/>\nnumbered with two 1s , three 2s and three 3s<br \/>\n{1,1,2,2,2,3,3,3}<br \/>\nThe number of favorable outcomes of spinning an odd number\u00a0 = 5<br \/>\nThey are {1,1,3,3,3}<br \/>\nTotal number of outcomes = 8<br \/>\nConsider O be the event of spinning an odd number<br \/>\nProbability P(O) = Number of favorable outcomes\/ Total number of outcomes<br \/>\nP(O) = 5\/8 =0.62<br \/>\nTherefore , the probability of spinning an odd number = 0.62<\/p>\n<p>Question 7.<br \/>\nspinning an even number<br \/>\nAnswer:<br \/>\nThe spinner is divided into 8 equal parts<br \/>\nnumbered with two 1s , three 2s and three 3s<br \/>\n{1,1,2,2,2,3,3,3}<br \/>\nThe number of favorable outcomes of spinning an even number = 3<br \/>\nThey are {2,2,2}<br \/>\nTotal number of outcomes = 8<br \/>\nConsider E be the event of spinning an even number<br \/>\nProbability P(E) = Number of favorable outcomes\/ Total number of outcomes<br \/>\nP(E) = 3\/8 = 0.37<\/p>\n<p>Question 8.<br \/>\nspinning a number greater than 0<br \/>\nAnswer:<br \/>\nThe spinner is divided into 8 equal parts<br \/>\nnumbered with two 1s , three 2s and three 3s<br \/>\n{1,1,2,2,2,3,3,3}<br \/>\nThe number of favorable outcomes of spinning a number greater than 0 =8<br \/>\nThey are {1,1,2,2,2,3,3,3}<br \/>\nTotal number of outcomes = 8<br \/>\nConsider S be the event of spinning a 1<br \/>\nProbability P(S) = Number of favorable outcomes\/ Total number of outcomes<br \/>\nP(S) = 8\/8 =1<\/p>\n<p>Question 9.<br \/>\nspinning a number less than 3<br \/>\nAnswer:<br \/>\nThe spinner is divided into 8 equal parts<br \/>\nnumbered with two 1s , three 2s and three 3s<br \/>\n{1,1,2,2,2,3,3,3}<br \/>\nThe number of favorable outcomes of spinning a number less than a 3 = 5<br \/>\nThey are {1,1,2,2,2}<br \/>\nTotal number of outcomes = 8<br \/>\nConsider T be the event of spinning a number less than a 3<br \/>\nProbability P(T) = Number of favorable outcomes\/ Total number of outcomes<br \/>\nP(T) = 5\/8 = 0.62<\/p>\n<p><strong>Describe the likelihood of the event given its probability.<\/strong><br \/>\nQuestion 10.<br \/>\nThere is a 0% chance of snow in July for Florida.<br \/>\nAnswer:<br \/>\nGiven , the probability = 0<br \/>\nSo the likelihood of the event is impossible<\/p>\n<p>Question 11.<br \/>\nThe probability that you are called on to answer a question in class is \\(\\frac{1}{25}\\).<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nThere is an 85% chance the bus is on time.<br \/>\nAnswer:<br \/>\nGiven, 85% chance = 0.85<br \/>\nSo, the probability is more likely to happen<\/p>\n<p>Question 13.<br \/>\nThe probability of flipping heads on a coin is 0.5.<br \/>\nAnswer:<br \/>\nGiven 0.5 = 50%<br \/>\nSo, the probability of flipping heads is may or may not occur<\/p>\n<p>Question 14.<br \/>\nDuring a basketball game, you record the number of rebounds from missed shots for each team. (a)Describe the likelihood that your team rebounds the next missed shot. (b) How many rebounds should your team expect to have in 15 missed shots?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28989\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-7.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability cr 7\" width=\"190\" height=\"78\" \/><br \/>\nAnswer:<br \/>\na.Total number of shots = 10<br \/>\nConsider M be the event of rebounds the next missed shot<br \/>\nThe probability\u00a0 = Number of missed shots \/ total number of trails<br \/>\nP(M) = 7\/10 = 0.7<br \/>\nTherefore , the likelihood that your team rebounds the next missed shot is likely to happen<\/p>\n<p>b.Total number of shots = 15<br \/>\nConsider S be the event of rebounds the your team misses the shot<br \/>\nprobability P(S) = Number of rebounds \/ total number of trails<br \/>\nP(S) = 7\/15 = 0.46<br \/>\nTherefore, the likelihood that the rebounds are expected to happen in 15 shots is not likely to occur<\/p>\n<p><strong>7.2 Experimental and Theoretical Probability (pp. 291\u2013298)<\/strong><br \/>\nLearning Target :Develop probability models using experimental and theoretical probability.<\/p>\n<p>The bar graph shows the results of spinning a spinner 100 times. Use the bar graph to find the experimental probability of the event.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28990\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-15.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability cr 15\" width=\"243\" height=\"190\" \/><br \/>\nQuestion 15.<br \/>\nspinning a 2<br \/>\nAnswer: 0.18<\/p>\n<p>Explanation :<br \/>\nTotal number of spins = 100<br \/>\nThe number of times 2 spun = 18<br \/>\nExperimental probability = Number of times an event occur \/ Total number of spins<br \/>\nConsider T be the event of spinning a 2<br \/>\nP(T) = 18\/100 =0.18<br \/>\nTherefore , experimental probability of spinning a 2 = 0.18<\/p>\n<p>Question 16.<br \/>\nspinning an even number<br \/>\nAnswer: 0.39<\/p>\n<p>Explanation:<br \/>\nTotal number of spins = 100<br \/>\nNumber of even numbers = 2<br \/>\nThey are {2,4}<br \/>\nThe number of times 2 spun = 18<br \/>\nThe number of times 4 spun = 21<br \/>\nTotal : 18+21 = 39<br \/>\nExperimental probability = Number of times an event occur \/ Total number of spins<br \/>\nConsider T be the event of spinning an even number<br \/>\nP(T) = 38\/100 =0.39<br \/>\nTherefore , experimental probability of spinning an even number = 0.39<\/p>\n<p>Question 17.<br \/>\nnot spinning a 5<br \/>\nAnswer: 0.81<br \/>\nTotal number of spins = 100<br \/>\nNumber of numbers other than 5 = 4<br \/>\nThey are {1,2,3,4}<br \/>\nThe number of times 1 spun = 20<br \/>\nThe number of times 2 spun = 18<br \/>\nThe number of times 3 spun = 22<br \/>\nThe number of times 4 spun = 21<br \/>\nTotal : 81<br \/>\nExperimental probability = Number of times an event occur \/ Total number of spins<br \/>\nConsider F be the event of not spinning a 5<br \/>\nP(F) = 81\/100 =0.81<br \/>\nTherefore , experimental probability of not spinning a 5 = 0.81<\/p>\n<p>Question 18.<br \/>\nspinning a number less than 3<br \/>\nAnswer:<br \/>\nTotal number of spins = 100<br \/>\nThe numbers less than 3 = 2<br \/>\nThey are {1,2}<br \/>\nThe number of times 1 spun = 20<br \/>\nThe number of times 2 spun = 18<br \/>\nTotal : 18 + 20 = 38<br \/>\nExperimental probability = Number of times an event occur \/ Total number of spins<br \/>\nConsider T be the event of spinning a number less than 3<br \/>\nP(T) = 38\/100 =0.38<br \/>\nTherefore , experimental probability of spinning a number less than 3\u00a0 = 0.38<\/p>\n<p>Question 19.<br \/>\nIn Exercise 16, how does the experimental probability of spinning an even number compare with the theoretical probability?<br \/>\nAnswer:<\/p>\n<p><strong>Use the spinner to find the theoretical probability of the event.<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28991\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-20.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability cr 20\" width=\"180\" height=\"154\" \/><br \/>\nQuestion 20.<br \/>\nspinning blue<br \/>\nAnswer:<br \/>\nThe spinner is divided into 8 equal parts<br \/>\nThey are numbered with three 1 s ,one 2 ,one 4 ,one 6 , one 8 , and one 10<br \/>\nAnd colored in 2 red , 2 blue , 2 purple and 2 orange in color<br \/>\nConsider , B be the event of spinning a blue<br \/>\nP(B) = 2\/8<br \/>\nP(B) = 0.25<\/p>\n<p>Question 21.<br \/>\nspinning a 1<br \/>\nAnswer:<br \/>\nThe spinner is divided into 8 equal parts<br \/>\nThey are numbered with three 1 s ,one 2 ,one 4 ,one 6 , one 8 , and one 10<br \/>\nConsider , O be the event of spinning a 1<br \/>\nP(O) = 3\/8<br \/>\nP(O) = 0.37<\/p>\n<p>Question 22.<br \/>\nspinning an even number<br \/>\nAnswer:<br \/>\nThe spinner is divided into 8 equal parts<br \/>\nThey are numbered with three 1 s ,one 2 ,one 4 ,one 6 , one 8 , and one 10<br \/>\nTotal number of even numbers = 5<br \/>\nThey are {2,4,6,8,10}<br \/>\nConsider , E be the event of spinning an even number<br \/>\nP(E) = 5\/8<br \/>\nP(E) = 0.62<\/p>\n<p>Question 23.<br \/>\nspinning a 4<br \/>\nAnswer:<br \/>\nThe spinner is divided into 8 equal parts<br \/>\nThey are numbered with three 1 s ,one 2 ,one 4 ,one 6 , one 8 , and one 10<br \/>\nConsider , F be the event of spinning a blue<br \/>\nP(F) = 1\/8<br \/>\nP(F) = 0.125<\/p>\n<p>Question 24.<br \/>\nThe theoretical probability of choosing a red grape from a bag of grapes is \\(\\frac{2}{9}\\). There are 8 red grapes in the bag. How many grapes are in the bag?<br \/>\nAnswer:<br \/>\nGiven theoretical probability = 2\/9<br \/>\nNumber of red grapes = 8<br \/>\nTotal number of grapes = x<br \/>\n8\/x = 2\/9<br \/>\n72 = 2x<br \/>\nx = 72\/2<br \/>\nx = 35<\/p>\n<p>Question 25.<br \/>\nThe theoretical probability of choosing Event A is \\(\\frac{2}{7}\\). What is the theoretical probability of not choosing Event A? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>7.3 Compound Events (pp. 299\u2013306)<\/strong><br \/>\nLearning Target: Find sample spaces and probabilities of compound events.<\/p>\n<p>Question 26.<br \/>\nYou have 6 bracelets and 15 necklaces. Find the number of ways you can wear one bracelet and one necklace.<br \/>\nAnswer:<br \/>\nNumber of bracelets = 6<br \/>\nNumber of necklaces = 15<br \/>\nAccording to fundamental counting principle,<br \/>\na x b = 6 x 15 = 90<br \/>\nTherefore, In 90 ways you can wear one bracelet and one necklace<\/p>\n<p>Question 27.<br \/>\nUse a tree diagram to find how many different home theater systems you can make from 6 DVD players,8 TVs, and 3 brands of speakers.<br \/>\nAnswer:<br \/>\nNumber of DVDs = 6<br \/>\nNumber of TVs = 8<br \/>\nNumber of brands of speaker = 3<br \/>\nTotal number of outcomes = 6 x 8 x 3 = 144<\/p>\n<p>Question 28.<br \/>\nA red, green, and blue book are on a shelf. You randomly pick one of the books. Without replacing the first book, you choose another book. What is the probability that you picked the red and blue book?<br \/>\nAnswer:<br \/>\nNumber of books in shelf = 3<\/p>\n<p>Question 29.<br \/>\nYou flip two coins and roll a number cube. What is the probability of flipping two tails and rolling an even number?<br \/>\nAnswer:<br \/>\nnumber of total outcomes for coin = 2<br \/>\nThe probability of flipping tails P(T ) = 1\/2<br \/>\nFor two coins , probability of flipping tails = 1\/2 x 2 = 1\/4<br \/>\nThe number of total outcomes for 6<br \/>\neven numbers = {2,4,6}<br \/>\nThe probability for flipping an even number = 3\/6 = 1\/2<br \/>\nSo, the probability of flipping two tails and rolling an even number<br \/>\n= 1\/4 x 1\/2 = 1\/8<\/p>\n<p>Question 30.<br \/>\nDescribe a compound event that has a probability between 50% and 80%.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\nYour science teacher sets up six flasks. Two of the flasks contain water and four of the flasks contain hydrogen peroxide. A reaction occurs when you add yeast to hydrogen peroxide. You add yeast to two of the flasks. What is the probability that at least one reaction will occur?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28992\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-31.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability cr 31\" width=\"229\" height=\"154\" \/><br \/>\nAnswer:<\/p>\n<p><strong>7.4 Simulations (pp. 307\u2013312)<\/strong><br \/>\nLearning Target: Design and use simulations to find probabilities of compound events.<\/p>\n<p>Question 32.<br \/>\nYou select a marble from two different bags. You have a 30% chance of choosing a blue marble from the first bag and a 70% chance of choosing a blue marble from the second bag. Design and use a simulation to estimate the probability that you choose a blue marble from both bags.<br \/>\nAnswer:<br \/>\nGiven , the chance of choosing blue marble from first bag =30%<br \/>\nThe chance of choosing blue marble from second bag = 70%<br \/>\n82 \u00a04 \u00a090 \u00a096 \u00a018 \u00a065 \u00a011 \u00a071 \u00a097 \u00a053<br \/>\n48 \u00a063<span style=\"font-size: 16px;\">\u00a032 \u00a054 \u00a052 \u00a017 \u00a014 \u00a05 \u00a083 \u00a050<br \/>\n<\/span><span style=\"font-size: 16px;\">61 \u00a036 \u00a010 \u00a081<\/span>\u00a058 \u00a084 \u00a09 \u00a080 \u00a094 \u00a095<br \/>\n15 \u00a042 \u00a02 \u00a045 \u00a068 \u00a064 \u00a033 38 \u00a012 \u00a060<br \/>\n35 \u00a016 \u00a021 \u00a099 \u00a059 \u00a055 \u00a022 \u00a020 \u00a037 \u00a087<br \/>\nLet the digits 1 through 3 in the tens place represents choosing blue marble from first bag<br \/>\nthe digits 1 and 7 in the ones place represent choosing blue marble from second bag<br \/>\nlet P(S) be the event choosing both blue marbles from both bags = 18\/50<br \/>\nTherefore, the experimental probability = 0.36 = 36%<\/p>\n<p>Question 33.<br \/>\nA cereal company is including a prize in each box. There are 5 different prizes, all of which are equally likely.<br \/>\na. Describe a simulation involving 50 trials that you can use to model the prizes in the next 3 boxes of cereal you buy.<br \/>\nb. Use your simulation to find the experimental probability that all three boxes contain a different prize.<br \/>\nAnswer:<br \/>\nGiven ,<br \/>\nThere are 5 different prizes, all of which are equally likely.<\/p>\n<p>Question 34.<br \/>\nIn the past month, your cell phone has lost its entire charge on 40% of days. Design and use a simulation to estimate the experimental probability that your cell phone loses its entire charge on exactly 2 of the next 5 days.<br \/>\nAnswer:<br \/>\nGiven,<br \/>\nCell phone has lost its entire charge on 40%<br \/>\nLet the numbers 1 through 40 represents possible<br \/>\n6 \u00a079 \u00a03 \u00a023 \u00a082<br \/>\n84 \u00a067 \u00a014 \u00a059 88<br \/>\n11 \u00a047 \u00a026<span style=\"font-size: 16px;\">\u00a068 \u00a018<br \/>\n<\/span><span style=\"font-size: 16px;\">\u00a069 \u00a091 \u00a051 \u00a056 \u00a042<br \/>\n<\/span><span style=\"font-size: 16px;\">\u00a015 \u00a099 \u00a058 \u00a092 \u00a062<br \/>\n<\/span><span style=\"font-size: 16px;\">\u00a013 \u00a041 \u00a055 \u00a017 \u00a035<br \/>\n<\/span><span style=\"font-size: 16px;\">\u00a028 \u00a054 \u00a085 \u00a097 \u00a065<br \/>\n<\/span><span style=\"font-size: 16px;\">\u00a098 \u00a057 \u00a071 \u00a073 \u00a038<br \/>\n<\/span><span style=\"font-size: 16px;\">\u00a089 \u00a090 \u00a087 \u00a039 \u00a072<br \/>\n<\/span><span style=\"font-size: 16px;\">\u00a019 \u00a08 \u00a021 \u00a045 \u00a031<br \/>\n<\/span>There are 2 or more successes in trails {1,3,6,10 }<br \/>\nThe experimental probability that your cell phone loses its entire charge on exactly 2 of the next 5 days = 4\/50<br \/>\nP(S) = 0.08 = 8%<\/p>\n<p>Question 35.<br \/>\nYou and your friends form a team in gym class. You have an 80% chance of winning a game of basketball and a 10% chance of winning a game of soccer. Design and use a simulation involving 50 randomly generated numbers to estimate the probability of winning both games.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28993\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Grade-7-Chapter-7-Probability-cr-35.png\" alt=\"Big Ideas Math Answer Key Grade 7 Chapter 7 Probability cr 35\" width=\"293\" height=\"168\" \/><br \/>\nAnswer:<br \/>\nGiven , The chance of winning a game of basket ball = 80%<br \/>\nThe probability of winning a soccer game = 10%<br \/>\n33 \u00a091 \u00a074 \u00a087 \u00a053 \u00a067 \u00a063 \u00a09 \u00a047 \u00a052 \u00a017 \u00a08<br \/>\n40 \u00a058 \u00a0100 \u00a011 \u00a044 \u00a020 \u00a049 \u00a072 \u00a060 \u00a066 \u00a079 \u00a051<br \/>\n69 \u00a073 \u00a076 \u00a043 \u00a077 \u00a097 \u00a02 \u00a093 \u00a012 \u00a036 \u00a06 \u00a086 \u00a092<span style=\"font-size: 16px;\"> 59<br \/>\n<\/span><span style=\"font-size: 16px;\">\u00a084 \u00a029 \u00a015 \u00a085 \u00a088 \u00a096 \u00a032 \u00a038 \u00a064 \u00a071 \u00a098 \u00a034<br \/>\n<\/span>Let the digits 1 through 8 in the tens place represents winning a basketball<br \/>\nLet digits 1 and 2 in the ones place represent winning a soccer game.<br \/>\nlet P(S) be the event of winning both the games = 7\/50<br \/>\nTherefore, the experimental probability = 0.14 = 14%<\/p>\n<h3><a id=\"Probability_Practice_Test\"><\/a>Probability Practice Test<\/h3>\n<p>You randomly choose one game piece. (a) Find the number of ways the event can occur. (b) Find the favorable outcomes of the event.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-29000\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-pt-1.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability pt 1\" width=\"376\" height=\"77\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-pt-1.png 376w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-pt-1-300x61.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><br \/>\nQuestion 1.<br \/>\nchoosing green<br \/>\nAnswer:<br \/>\nNumber of game pieces = 10<br \/>\nIn which , 3 are yellow , 2 blue , 2 red and 1 are green in color<br \/>\nProbability P(G)= Number of favorable outcomes \/ Total number of outcomes<br \/>\nConsider G be the event of choosing green<br \/>\nP(G) = 1 \/ 10= 0..1<br \/>\nTherefore, the probability of choosing green = 0.1<\/p>\n<p>Question 2.<br \/>\nchoosing not yellow<br \/>\nAnswer:<br \/>\nNumber of game pieces = 10<br \/>\nIn which , 3 are yellow , 2 blue , 2 red and 1 are green in color<br \/>\nNumber of not yellow colors = 5<br \/>\nThey are { blue , green , red }<br \/>\nP(N) = Number of favorable outcomes \/ Total umber of outcomes<br \/>\nP(N) = 5\/10 = 0.5<br \/>\nTherefore, the probability of not choosing yellow= 0.5<\/p>\n<p>Find the sample space and the total number of possible outcomes.<br \/>\nQuestion 3.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-29001\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-pt-3.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability pt 3\" width=\"201\" height=\"99\" \/><br \/>\nAnswer:<br \/>\nNumber of SPF = 5<br \/>\nNumber of types = 3<br \/>\nThe total number of outcomes = 5 x 3 =15<br \/>\nTherefore number of possible outcomes = 15<br \/>\n{10,lotion} {15,lotion} {30, lotion} {45, lotion} {50, lotion}<br \/>\n{10, spray } {15, spray} {30, spray } {45, spray} {50, spray}<br \/>\n{10,gel} {15, gel} {30 , gel} {45 ,gel} {50 , gel}<\/p>\n<p>Question 4.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-29002\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-pt-4.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability pt 4\" width=\"243\" height=\"98\" \/><br \/>\nAnswer:<br \/>\nNumber of types = 4<br \/>\nNumber of colors = 3<br \/>\nTotal number of possible outcomes = 4 x3 = 12<br \/>\n{Basic display, Black\u00a0 } {Basic display, white } {Basic display , silver}<br \/>\n{Scientific, Black} {Scientific, white} {Scientific , silver}<br \/>\n{Graphing ,black } {Graphing , white} {Graphing , silver}<\/p>\n<p><strong>Use the bar graph to find the experimental probability of the event.<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-29003\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-pt-5.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability pt 5\" width=\"266\" height=\"174\" \/><br \/>\nQuestion 5.<br \/>\nrolling a 1 or a 2<br \/>\nAnswer:<br \/>\nTotal Number of rolls = 90<br \/>\nThe number of times 1 rolled = 12<br \/>\nThe number of times 2 rolled = 18<br \/>\nTotal = 30<br \/>\nThe probability of rolling a 1 or a 2 =<br \/>\nP(R) = 30\/90<br \/>\nP(R) = 0.33<\/p>\n<p>Question 6.<br \/>\nrolling an odd number<br \/>\nAnswer:<br \/>\nThe number of odd numbers = 3<br \/>\nThey are {1,3,5}<br \/>\nNumber of times 1 rolled = 12<br \/>\nNumber of times 3 rolled = 14<br \/>\nNumber of times 5 rolled =\u00a0 16<br \/>\nTotal : 12 + 14 + 16 =42<br \/>\nConsider O be the event of spinning an odd number<br \/>\nP(O) = 42\/90 = 0.46<\/p>\n<p>Question 7.<br \/>\nnot rolling a 5<br \/>\nAnswer:<br \/>\nThe total number of rolls = 90<br \/>\nThe number of\u00a0 numbers other than 5 are =5<br \/>\nThey are 1,2,3,4,6<br \/>\nThe number of times 1 rolled = 12<br \/>\nThe number of times 2 rolled = 18<br \/>\nThe number of times 3 rolled = 14<br \/>\nThe number of times 4 rolled = 17<br \/>\nThe number of times 6 rolled = 13<br \/>\nTotal = 74<br \/>\nThe probability of rolling not 5 = 74\/ 90<br \/>\nP(G) = 0.82<\/p>\n<p>Question 8.<br \/>\nrolling a number less than 7<br \/>\nAnswer:<br \/>\nThe total number of rolls = 90<br \/>\nThe number of\u00a0 numbers less than 7 are = 6<br \/>\nThey are 1,2,3,4,5,6<br \/>\nThe number of times 1 rolled = 12<br \/>\nThe number of times 2 rolled = 18<br \/>\nThe number of times 3 rolled = 14<br \/>\nThe number of times 4 rolled = 17<br \/>\nThe number of times 5 rolled = 16<br \/>\nThe number of times 6 rolled = 13<br \/>\nTotal = 90<br \/>\nThe probability of rolling a number less than 7 = 90\/ 90<br \/>\nP(L) =1<\/p>\n<p><strong>Use the spinner to find the theoretical probability 93of the event(s).<\/strong><br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-29004\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-pt-9.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability pt 9\" width=\"148\" height=\"134\" \/><br \/>\nQuestion 9.<br \/>\nspinning an even number<br \/>\nAnswer:<br \/>\nThe spinner is divided into 9 equal parts<br \/>\nNumbered as {1,2,3,4,5,6,7,8,9}<br \/>\nSo, total number of outcomes = 9<br \/>\nNumber of even numbers = 4<br \/>\nThey are {2,4,6,8}<br \/>\nTheoretical probability = Number of favorable outcomes \/ Total number of outcomes<br \/>\nConsider , E be the event of choosing an even number<br \/>\nP(E) = 4\/ 9 = 0.44<br \/>\nTherefore , the probability for spinning an even number =0.44<\/p>\n<p>Question 10.<br \/>\nspinning a 1 and then a 2<br \/>\nAnswer:<br \/>\nThe spinner is divided into 9 equal parts<br \/>\nNumbered as {1,2,3,4,5,6,7,8,9}<br \/>\nSo, total number of outcomes = 9<br \/>\nThe probability of spinning 1 = 1\/9<br \/>\nThen the probability of spinning 2 = 1\/9<br \/>\nTotal probability of the event spinning a 1 and then 2 = 1\/9 x 1\/9<br \/>\nTotal P(B) = 1\/ 81<br \/>\nTherefore , the probability of spinning a 1 and then 2 = 0.012<\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-29005\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-pt-11.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability pt 11\" width=\"202\" height=\"123\" \/><br \/>\nQuestion 11.<br \/>\nYou randomly choose one of the pens shown. What is the theoretical probability of choosing a black pen?<br \/>\nAnswer:<br \/>\nTheoretical probability = Number of favorable outcomes \/ Total number of outcomes<br \/>\nTotal number of pens = 5<br \/>\nNumber of black pens = 2<br \/>\nConsider B be the event of choosing a black pen<br \/>\nP(B) = 2\/5 = 0.4<br \/>\nTherefore, the theoretical probability of choosing a black pen = 0.4<\/p>\n<p>Question 12.<br \/>\nYou randomly choose one of the pens shown. Your friend randomly chooses one of the remaining pens. What is the probability that you and your friend both choose a blue pen?<br \/>\nAnswer:<br \/>\nTotal number of pens = 5<br \/>\nNumber of blue pens = 2<br \/>\nThe probability that you and your friend both choose a blue pen<br \/>\nP(B) = 2\/5<br \/>\nP(B) = 0.4<\/p>\n<p>Question 13.<br \/>\nThere is an 80% chance of a thunderstorm on Saturday. Describe the likelihood that there is not a thunderstorm on Saturday.<br \/>\nAnswer:<br \/>\nGiven probability 80% = 0.8<br \/>\nNot thunder storm probability = 20 % = 0.2<br \/>\nThe likelihood of the event is not likely to happen<\/p>\n<h3><a id=\"Probability_Cumulative_Practice\"><\/a>Probability Cumulative Practice<\/h3>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28994\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-cp-1.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability cp 1\" width=\"311\" height=\"355\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-cp-1.png 311w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-cp-1-263x300.png 263w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><br \/>\nQuestion 1.<br \/>\nA school athletic director asked each athletic team member to name his or her favorite professional sports team. The results are below:<\/p>\n<ul>\n<li>D.C.United: 3<\/li>\n<li>Florida Panthers: 8<\/li>\n<li>Jacksonville Jaguars: 26<\/li>\n<li>Jacksonville Sharks: 7<\/li>\n<li>Miami Dolphins: 22<\/li>\n<li>Miami Heat: 15<\/li>\n<li>Miami Marlins: 20<\/li>\n<li>Minnesota Lynx: 4<\/li>\n<li>New YorkKnicks: 5<\/li>\n<li>Orlando Magic: 18<\/li>\n<li>Tampa Bay Buccaneers: 17<\/li>\n<li>Tampa Bay Lightning: 12<\/li>\n<li>Tampa Bay Rays: 28<\/li>\n<li>Other: 6<\/li>\n<\/ul>\n<p>One athletic team member is picked at random. What is the likelihood that this team member\u2019s favorite professional sports team is not located in Florida?<br \/>\nA. certain<br \/>\nB. likely, but not certain<br \/>\nC. unlikely, but not impossible<br \/>\nD. impossible<br \/>\nAnswer: B<br \/>\n13\/14 = 0.92<br \/>\nThe likelihood of the event is likely, but not certain<\/p>\n<p>Question 2.<br \/>\nEach student in your class voted for his or her favorite day of the week. Their votes are shown in the circle graph:<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28995\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-cp-2.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability cp 2\" width=\"353\" height=\"194\" srcset=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-cp-2.png 353w, https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-cp-2-300x165.png 300w\" sizes=\"(max-width: 353px) 100vw, 353px\" \/><br \/>\nA student from your class is picked at random. What is the probability that this student\u2019s favorite day of the week is Sunday?<br \/>\nAnswer:<br \/>\nTotal number of students =30<br \/>\nTotal number of Sunday = 6<br \/>\nThe probability of that this student\u2019s favorite day of the week is Sunday<br \/>\nP(S) = 6\/30<br \/>\n= 0.2<\/p>\n<p>Question 3.<br \/>\nWhat value makes the equation 11 &#8211; 3x = &#8211; 7 true?<br \/>\nF. &#8211; 6<br \/>\nG. \\(-\\frac{4}{3}\\)<br \/>\nH. 6<br \/>\nI. 54<br \/>\nAnswer:\u00a0 F<\/p>\n<p>Explanation:<br \/>\n11 &#8211; 3x = -7<br \/>\nConsider the value of x = -6<br \/>\nL.H.S\u00a0 = 11-3X<br \/>\n11 &#8211; 3 (-6)<br \/>\n11 &#8211; 18<br \/>\n= -4<br \/>\nL.H.S = R.H.S<br \/>\nTherefore, the value of x =-6<\/p>\n<p>Question 4.<br \/>\nYour friend solved the proportion in the box below.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28996\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-cp-4.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability cp 4\" width=\"207\" height=\"191\" \/><br \/>\nWhat should your friend do to correct the error that he made?<br \/>\nA. Add 40 to 16 and 27 to p.<br \/>\nB. Subtract 16 from 40 and 27 from p.<br \/>\nC. Multiply 16 by 27 and p by 40.<br \/>\nD. Divide 16 by 27 and p by 40.<br \/>\nAnswer: C<br \/>\nMultiply 16 by 27 and p by 40<\/p>\n<p>Question 5.<br \/>\nWhich value is a solution of the inequality?<br \/>\n3 &#8211; 2y &lt; 7<br \/>\nF. &#8211; 6<br \/>\nG. &#8211; 3<br \/>\nH. &#8211; 2<br \/>\nI. &#8211; 1<br \/>\nAnswer: H<br \/>\n3- 2y &lt; 7 =0<br \/>\n3-2y &gt;7<br \/>\n-2y &gt; 7-3<br \/>\n-2y &gt;4<br \/>\ny &gt; -4\/2<br \/>\ny &gt; -2<\/p>\n<p>Question 6.<br \/>\nA spinner is divided into eight equal sections, as shown. You spin the spinner twice. What is the probability that the arrow will stop in a yellow section both times?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28997\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-cp-6.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability cp 6\" width=\"284\" height=\"162\" \/><br \/>\nAnswer:<br \/>\nThe spinner is divided 8 equal parts<br \/>\nIn which , 3 are red , 2 are blue, 2 are yellow and 1 part is in pink color<br \/>\nso the probability of landing on yellow would be<br \/>\nP(Y) = 3\/8 on first spun.<br \/>\nTherefore, for spinning the spinner twice then the probability of landing it on yellow would be<br \/>\nP(Y) = (3\/8)\/2<br \/>\nP(Y) =3\/16<\/p>\n<p>Question 7.<br \/>\nA pair of running shoes is on sale for 25% off the original price. Which price is closest to the sale price of the running shoes?<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28998\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-cp-7.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability cp 7\" width=\"212\" height=\"155\" \/><br \/>\nA. $93<br \/>\nB. $99<br \/>\nC. $124<br \/>\nD. $149<br \/>\nAnswer: A<\/p>\n<p>Explanation :<br \/>\nOriginal price = $122.76<br \/>\nPercent of discount = 25% = 0.25<br \/>\nThe amount of discount :<br \/>\nAmount of discount = Discount x original price<br \/>\n= 0.25 x $125<br \/>\n= $30.39<br \/>\nSale price :<br \/>\nSale price = Original price &#8211; discount<br \/>\n= $122.76 &#8211; $30.39<br \/>\n= $92.07<br \/>\nIt is very close to the sale price of the running shoes = $ 93<\/p>\n<p>Question 8.<br \/>\nThe value of a baseball card was $6 when it was sold. The value of this card is now $15. What is the percent increase in the value of the card?<br \/>\nF. 40%<br \/>\nG. 90%<br \/>\nH. 150%<br \/>\nI. 250%<br \/>\nAnswer: H<br \/>\nGiven,<br \/>\nOriginal price of the basket ball\u00a0 = $6<br \/>\nNew price = $15<br \/>\nThe original price increases so, the percent of change is called percent of increase<br \/>\nPercent of increase = New price &#8211; original price\/ Original price<br \/>\nOn substituting ,<br \/>\n= 15 &#8211; 6\/ 6<br \/>\n= 9 \/ 6<br \/>\n=3\/2<br \/>\nOn multiplying with 100<br \/>\n= 3\/2 x 100<br \/>\n= 150%<br \/>\nTherefore , the percent increase in the value of the card = 150%<\/p>\n<p>Question 9.<br \/>\nYou roll a number cube twice. You want to roll two even numbers.<br \/>\n<img decoding=\"async\" loading=\"lazy\" class=\"alignnone size-full wp-image-28999\" src=\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-7th-Grade-Chapter-7-Probability-cp-9.png\" alt=\"Big Ideas Math Answers 7th Grade Chapter 7 Probability cp 9\" width=\"77\" height=\"67\" \/><br \/>\nPart A Find the number of favorable outcomes and the number of possible outcomes of each roll.<br \/>\nPart B Find the probability of rolling two even numbers. Explain your reasoning.<br \/>\nAnswer:<br \/>\nPart A :<br \/>\nThe even numbers on a number cube are 2, 4, and 6<br \/>\nThe favorable outcomes for 2 are =3<br \/>\nThey are : 2 and 2 , 2 and 4 , 2 and 6<br \/>\nThe favorable outcomes for 4 are =3<br \/>\nThey are : 4 and 2 , 4 and 4 , 4 and 6<br \/>\nThe favorable outcomes for 6 are =3<br \/>\nThey are : 6 and 2 , 6 and 4 , 6 and 6<br \/>\nSo,\u00a0 total number favorable outcomes = 9<br \/>\nThere are 6 outcomes for each cube so there are 6(6) = 36 total outcomes.<\/p>\n<p>Part B :<br \/>\nThere are 9 favorable outcomes of a total of 36 outcomes<br \/>\nSo, the probability is 9\/36 = 1\/4<\/p>\n<p>Question 10.<br \/>\nYou put $600 into an account. The account earns 5% simple interest per year. What is the balance after 4 years?<br \/>\nA. $120<br \/>\nB. $720<br \/>\nC. $1800<br \/>\nD. $12,600<br \/>\nAnswer: B<br \/>\nSimple interest = principle x annual rate of interest x Time<br \/>\nI = P x r x t<br \/>\n5% = 0.5<br \/>\nI = 600 x 0.05 x 4<br \/>\nI = $120<br \/>\nThe interest earned = $120<br \/>\nThe balance after 4 years = principle + Interest<br \/>\n= 600 + 120<br \/>\n=$720<\/p>\n<p>Question 11.<br \/>\nYou are comparing the prices of four boxes of cereal. Two of the boxes contain free extra cereal.<\/p>\n<ul>\n<li>Box F costs $3.59 and contains 16 ounces.<\/li>\n<li>Box G costs $3.79 and contains 16 ounces, plus an additional 10% for free.<\/li>\n<li>Box H costs $4.00 and contains 500 grams.<\/li>\n<li>Box\u00a0 I costs $4.69 and contains 500 grams, plus an additional 20% for free.<\/li>\n<\/ul>\n<p>Which box has the least unit cost?<br \/>\nF. Box F<br \/>\nG. Box G<br \/>\nH. Box H<br \/>\nI. Box I<br \/>\nAnswer: Box G<\/p>\n<p>Explanation :<br \/>\nBox F<br \/>\n<span style=\"font-size: 16px;\">The unit cost of box F = 3.59\/16<br \/>\n<\/span><span style=\"font-size: 16px;\">The unit cost = $0.224 per ounces<br \/>\n<\/span><span style=\"font-size: 16px;\">Box G<br \/>\n<\/span><span style=\"font-size: 16px;\">Given 10% free<br \/>\n<\/span><span style=\"font-size: 16px;\">Which means, 10% = 16.01 = 0.6 ounces<br \/>\n<\/span><span style=\"font-size: 16px;\">The unit cost box G = $3.79 \/ 16 +0.6<br \/>\n<\/span><span style=\"font-size: 16px;\">=$0.215 ounces<br \/>\n<\/span>Box H<br \/>\nGiven, 500 grams<br \/>\nWhich means , 500\/28.35 = 17. 64 ounces<\/p>\n<div>The unit cost for box H = $4.00\/ 17.64<\/div>\n<div>= 0.227 ounces<\/div>\n<div>Box I<\/div>\n<div>Given 500 grams and 20 % additional<\/div>\n<div>\n<div>Which means , 500\/28.35 = 17. 64 ounces<\/div>\n<div>20% = 17.64 .02 = 3.53 ounces<\/div>\n<div>The unit cost = 4.69\/ 17.64+3.54<\/div>\n<div>= 0.222 ounces<\/div>\n<div>Therefore, Box G has the least unit cost .<\/div>\n<div><em>Final Words:<\/em><\/div>\n<\/div>\n<header>\n<section class=\"top\">\n<section class=\"object-ratings-wrap\">\n<section class=\"object-ratings large animatable solutions\">\n<div class=\"score\">We wish the information prevailed here is helpful for all the students of grade 7. For any doubts post the comments in the below comment section. We will try to clarify your doubts as early as possible.<\/div>\n<\/section>\n<\/section>\n<\/section>\n<\/header>\n","protected":false},"excerpt":{"rendered":"<p>In order to solve real-life mathematical problems, students must understand the concept behind the question. You have to know what is probability. This is the most interesting chapter among all the grade 7 chapters. Download Free Pdf of Big Ideas Math Answers Grade 7 Chapter 7 Probability to practice the exercise and homework problems. 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