\n| <\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Answer:
\nAnswers will vary depending on the outcomes when the student plays the game.<\/p>\n Exercise 4.
\nIf you changed the numbers assigned to the descriptions, was your score better than Alan\u2019s score? Did you expect your score to be better? Explain. If you did not change the numbers from those that Alan assigned, explain why you did not change them.
\nAnswer:
\nNote: This question provides students on opportunity to begin explaining the strategy they ore using in this game. Anticipate that in most coses students are assigning the larger numbers (the 5 or the 4) to the outcomes they think are most likely.<\/p>\n At this point in the lesson, students have not been asked to calculate the actual probabilities of the events of interest. However, some students may have already calculated or estimated the probabilities. Anticipate that students change the assignment of numbers to try to improve their scores.<\/p>\n As students discuss strategies for assigning numbers based on whkh events are most likely to occur, they are also
\nevaluating the thinking of others.<\/p>\n Exercise 5.
\nSpinning Spinner 1 and drawing a card from the card bag is a chance experiment. One possible outcome of this experiment is (1, Blue-A). Recall that the sample space for a chance experiment is the set of all possible outcomes. What is the sample space for the chance experiment of Scenario Card 1?
\nAnswer:
\nThe sample space consists of 18 outcomes.
\n((1, Blue-A), (1, Blue-B), (1, Blue-C), (1, Blue-D), (1, Red-E), (1, Red-F), (2, Blue-A), (2, Blue-B), (2, Blue-C), (2, Blue-D), (2, Red-E), (2, Red-F), (3, Blue-A), (3, Blue-B), (3, Blue-C), (3, Blue-D), (3,Red-E), (3, Red-F)).<\/p>\n Exercise 6.
\nAre the outcomes in the sample space equally likely? Explain your answer.
\nAnswer:
\nYes, each outcome is equally likely to occur because the spinner is equally likely to land in any of the three segments, and each of the six cards is equally likely to be selected. The selection of a card and the result of spinning the spinner do not depend on each other, so the 18 outcomes in the sampk space should be equally likely.<\/p>\n Exercise 7.
\nRecall that an event is a collection of outcomes from the sample space. One event of interest for someone with Scenario Card 1 is \u201codd number on Spinner 1 and a red card.\u201d What are the outcomes that make up this event? List the outcomes of this event in the first row of Table 1 (see Exercise 9).
\nAnswer:
\nSee the completed chart in Exercise 9.<\/p>\n Exercise 8.
\nWhat is the probability of getting an odd number on Spinner 1 and picking a red card from the card bag? Also enter this probability in Table 1 (see Exercise 9).
\nAnswer:
\nSee the completed table in Exercise 9. Direct students to write their probabilities as fractions or as decimals. Fractions do not need to be reduced, as the unreduced fractions are meaningful based on the context.<\/p>\n Exercise 9.
\nComplete Table 1 by listing the outcomes for the other events and their probabilities based on the chance experiment for this scenario card.<\/p>\n \n\n\n| Event<\/td>\n | Outcomes<\/td>\n | Probability<\/td>\n<\/tr>\n | \nOdd number on Spinner 1
\nand a red card from the card
\nbag<\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| Odd number on Spinner 1<\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \nOdd number on Spinner 1
\nand a blue card from the
\ncard bag<\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \nEven number on Spinner 1
\nor a red card from the card
\nbag<\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \nNot picking a blue card from
\nthe card bag<\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Answer:
\nThe following table organizes the responses to Exercises 7 – 9:<\/p>\n \n\n\n| Event<\/td>\n | Outcomes<\/td>\n | Probability<\/td>\n<\/tr>\n | \n| Odd number on Spinner 1 and a red card from the card bag<\/td>\n | Note:\u00a0 If students struggle with the \u201cand\u201d language, discuss the outcomes with students.<\/p>\n (, Red-E), (, Red-F), (, Red-E),
\n(, Red-F)<\/td>\n | The probability is, which is approximately .<\/p>\n Assign point to this event.<\/td>\n<\/tr>\n | \n| Odd number on Spinner 1<\/p>\n <\/td>\n | Note:\u00a0 Students may indicate that the probability of this outcome is the same as the probability of just getting an odd number on the spinner without considering the color of the card selected.<\/p>\n (, Blue-A), (, Blue-B), (, Blue-C),
\n(, Blue-D), (, Red-E), (, Red-F),
\n(, Blue-A), (, Blue-B), (, Blue-C),
\n(, Blue-D), (, Red-E), (, Red-F)<\/td>\n | The probability is or, which is approximately.<\/p>\n Assign points to this event.<\/td>\n<\/tr>\n | \n| Odd number on Spinner 1 and a blue card from the card bag<\/td>\n | (, Blue-A), (, Blue-B), (, Blue-C),
\n(, Blue-D), (, Blue-A), (, Blue-B),
\n(, Blue-C), (, Blue-D)<\/td>\n | The probability is, which is approximately.<\/p>\n Assign \u00a0points to this event.<\/td>\n<\/tr>\n | \n| Even number on Spinner 1 or a red card from the card bag<\/td>\n | Note:\u00a0 This event involves the \u201cor.\u201d\u00a0 Make sure students identify all of the outcomes that apply.\u00a0 This is an excellent event to discuss with students.<\/p>\n (, Red-E), (, Red-F), (, Blue-A),
\n(, Blue-B), (, Blue-C), (, Blue-D),
\n(, Red-E), (, Red-F), (, Red-E),
\n(, Red-F)<\/td>\n | The probability is, which is approximately.<\/p>\n Assign points to this event.<\/td>\n<\/tr>\n | \n| Not picking a blue card from the card bag<\/td>\n | Note:\u00a0 Although formally defined in Lesson 3, this is an example of the complement of the event \u201cpicking a blue card.\u201d\u00a0 An informal discussion of the word \u201ccomplement\u201d may be considered; however, it is not necessary at this time.<\/p>\n (, Red-E), (, Red-F), (, Red-E),
\n(, Red-F), (, Red-E), (, Red-F)<\/td>\n | The probability is, which is approximately.<\/p>\n Assign \u00a0points to this event.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Exercise 10.
\nBased on the above probabilities, how would you assign the numbers 1 – 5 to each of the game descriptions? Explain.
\nAnswer:
\nIf players assigned the points based on a 5 assigned to the event most likely to occur, followed by 4, etc., then there would be changes made to the assignment of points.<\/p>\n Exercise 11.
\nIf you changed any of the points assigned to the game descriptions, play the game again at least three times and record your final scores for each game. Do you think you have the best possible assignment of numbers to the events for this scenario card?<\/p>\n If you did not change the game descriptions, also play the game so that you have at least three final scores. Compare your scores with scores of other members of your class. Do you think you have the best assignment of numbers to the events for this scenario card?<\/p>\n \n\n\n| Turn<\/td>\n | Outcome from
\nSpinner 1<\/td>\n | Outcome from the
\nCard Bag<\/td>\n | Points Based on the
\nAssignment of Points in Exercise 10<\/td>\n<\/tr>\n | \n| 1<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 2<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 3<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 4<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 5<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Answer:
\nAnswers will vary. A good way to discuss this question with students is to compare the score Alan received with his assignment of points and the scores students received based on their assignments of points. Based on the assignment of points described in Exercise 10, one possible student response is shown below.<\/p>\n \n\n\n| Turn<\/td>\n | Outcome from
\nSpinner 1<\/td>\n | Outcome from the
\nCard Bag<\/td>\n | Points Based on the
\nAssignment of Points in Exercise 10<\/td>\n<\/tr>\n | \n| 1<\/td>\n | 2<\/td>\n | Blue<\/td>\n | 4<\/td>\n<\/tr>\n | \n| 2<\/td>\n | 1<\/td>\n | Red<\/td>\n | 5<\/td>\n<\/tr>\n | \n| 3<\/td>\n | 1<\/td>\n | Red<\/td>\n | 5<\/td>\n<\/tr>\n | \n| 4<\/td>\n | 3<\/td>\n | Blue<\/td>\n | 5<\/td>\n<\/tr>\n | \n| 5<\/td>\n | 2<\/td>\n | Blue<\/td>\n | 4<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n The final score for the above five turns is 23 points. This is a better score than Alan received from his assignment of points.<\/p>\n Exercise 12.
\nWhy might you not be able to answer the question of whether or not you have the best assignments of numbers to the game descriptions with at least three final scores?
\nAnswer:
\nTo decide the best assignment of points involves playing the game many times.
\nNote: Use this question to point out that probability is a long run relative frequency. For this example, to get a good sense of the probabilities, students would need to play the game many times.<\/p>\n Exercise 13.
\nWrite your answers to the following questions independently, and then share your responses with a neighbor:<\/p>\n a. How did you make decisions about what to bet on?
\nAnswer:
\nAnswers will vary. I calculated the probability of each outcome and bet in the order of probability, 5 (greatest) to 1 (least). I used probability but changed a few bets based on the earlier outcomes.<\/p>\n b. How do the ideas of probability help you make decisions?
\nAnswer:
\nAnswers will vary. Calculating probability gives you a good idea of the number of times on outcome will occur and helps you make better decisions.<\/p>\n Eureka Math Algebra 2 Module 4 Lesson 1 Problem Set Answer Key<\/h3>\nConsider a second scenario card that Alan created for his game:<\/p>\n Scenario Card 2
\nTools: Spinner 1<\/p>\n Spinner 2: a spinner with six equal sectors (Place the number 1 in a sector, the number 2 in a second sector, the number 3 in a third sector, the number 4 in a fourth sector, the number 5 in a fifth sector, and the number 6 in the last sector.)<\/p>\n Directions (chance experiment): Spin Spinner 1, and spin Spinner 2. Record the number from Spinner 1, and record the number from Spinner 2.<\/p>\n Five Events of Interest:<\/p>\n \n\n\n| \n Outcome is an odd number on
\nSpinner 2<\/p>\n<\/td>\n | Outcome is an odd number on Spinner 1 and an even number on Spinner 2.<\/td>\n | Outcome is the sum of 7 from the numbers received from Spinner 1 and
\nSpinner 2.<\/td>\n | Outcome is an even number on
\nSpinner 2.<\/td>\n | \n Outcome is the sum of 2 from the numbers received from Spinner 1 and
\nSpinner 2.<\/p>\n<\/td>\n<\/tr>\n | \n| <\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Player:
\nScoring Card for Scenario 2:<\/p>\n \n\n\n| Turn<\/td>\n | Outcome from Spinner 1<\/td>\n | Outcome for Spinner 2<\/td>\n | Points<\/td>\n<\/tr>\n | \n| 1<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 2<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 3<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 4<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 5<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Question 1.
\nPrepare Spinner 1 and Spinner 2 for the chance experiment described on this second scenario card. (Recall that Spinner 2 has six equal sectors.)
\nAnswer:
\nPrepare Spinner 2 as described. You can use the same Spinner 1 used for Scenario Card 1.<\/p>\n Question 2.
\nWhat is the sample space for the chance experiment described on this scenario card?
\nAnswer:
\nThere are 18 outcomes on this scenario card. Students can list all of the outcomes or describe them. Here is the list (the first number is the outcome from Spinner 1, and the second number is the outcome from Spinner 2);
\n(1, 1), (1,2), (1,3), (1,4), (1,5), (1,6), (2, 1), (2,2), (2,3), (2,4), (2.5), (2,6), (3, 1), (3,2), (3,3), (3,4), (3,5), (3,6)<\/p>\n Question 3.
\nBased on the sample space, determine the outcomes and the probabilities for each of the events on this scenario card. Complete the table below.<\/p>\n \n\n\n| Event<\/td>\n | Outcomes<\/td>\n | Probability<\/td>\n<\/tr>\n | \nOutcome is an odd number on
\nSpinner 2.<\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \nOutcome is an odd number on
\nSpinner 1 and an even number
\non Spinner 2.<\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \nOutcome is the sum of 7 from
\nthe numbers received from
\nSpinner 1 and Spinner 2.<\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \nOutcome is an even number on
\nSpinner 2.<\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \nOutcome is the sum of 2 from
\nthe numbers received from
\nSpinner 1 and Spinner 2.<\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Answer:
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Algebra-2-Module-4-Lesson-1-Problem-Set-Answer-Key-3.png\") <\/p>\n Note that although each event is different, some events are subsets of another event. As a result, students want to assign a larger number to the event with more outcomes. Expect that students obtain scores of 4 or 5 for each turn. As an extension, students may be asked to revise the descriptions of the events on the strategy cards in order to make the game more challenging.<\/p>\n Question 4.
\nAssign the numbers 1 – 5 to the events described on the scenario card.
\nAnswer:
\nThe following assignments would be based on the 5 assigned to the event with the greatest probability (the most likely outcome), to the event with the next largest, etc.:<\/p>\n Five Events of Interest: Scenario 2<\/p>\n \n\n\nOutcome is an odd number on
\nSpinner 2.<\/td>\n | Outcome is an odd number on Spinner 1 and an even number on
\nSpinner 2.<\/td>\n | Outcome is the
\nsum of 7 from the numbers received from Spinner 1 and
\nSpinner 2.<\/td>\n | Outcome is an even number on
\nSpinner 2.<\/td>\n | Outcome is the
\nsum of 2 from the numbers received from Spinner 1 and
\nSpinner 2.<\/td>\n<\/tr>\n | \n| <\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Answer:<\/p>\n \n\n\nOutcome is an odd number on
\nSpinner 2.<\/td>\n | Outcome is an odd number on Spinner 1 and an even number on
\nSpinner 2.<\/td>\n | Outcome is the
\nsum of 7 from the numbers received from Spinner 1 and
\nSpinner 2.<\/td>\n | Outcome is an even number on
\nSpinner 2.<\/td>\n | Outcome is the
\nsum of 2 from the numbers received from Spinner 1 and
\nSpinner 2.<\/td>\n<\/tr>\n | \n| 4<\/td>\n | 3<\/td>\n | 2<\/td>\n | 5<\/td>\n | 1<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Question 5.
\nDetermine at least three final scores based on the numbers you assigned to the events.
\nPlayer: Scott<\/p>\n \n\n\n| Trial<\/td>\n | Outcome from Spinner 1<\/td>\n | Outcome for Spinner 2<\/td>\n | Points (see Problem 4)<\/td>\n<\/tr>\n | \n| 1<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 2<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 3<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 4<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 5<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Player: Scott<\/p>\n \n\n\n| Trial<\/td>\n | Outcome from Spinner 1<\/td>\n | Outcome for Spinner 2<\/td>\n | Points (see Problem 4)<\/td>\n<\/tr>\n | \n| 1<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 2<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 3<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 4<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 5<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Player: Scott<\/p>\n \n\n\n| Trial<\/td>\n | Outcome from Spinner 1<\/td>\n | Outcome for Spinner 2<\/td>\n | \n Points (see Problem 4)<\/p>\n<\/td>\n<\/tr>\n | \n| 1<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 2<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 3<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 4<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| 5<\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Answer:
\nResponses will vary. Provided are three final scores based on outcomes from carrying out the game.<\/p>\n Player Scott:<\/p>\n \n\n\n| Trial<\/td>\n | Outcome from Spinner 1<\/td>\n | Outcome for Spinner 2<\/td>\n | Points (see Problem 4)<\/td>\n<\/tr>\n | \n| 1<\/td>\n | 2<\/td>\n | 6<\/td>\n | 5<\/td>\n<\/tr>\n | \n| 2<\/td>\n | 1<\/td>\n | 5<\/td>\n | 4<\/td>\n<\/tr>\n | \n| 3<\/td>\n | 2<\/td>\n | 6<\/td>\n | 5<\/td>\n<\/tr>\n | \n| 4<\/td>\n | 3<\/td>\n | 3<\/td>\n | 4<\/td>\n<\/tr>\n | \n| 5<\/td>\n | 2<\/td>\n | 2<\/td>\n | 5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Final Score: 23 Points<\/p>\n Player: Scott<\/p>\n \n\n\n| Trial<\/td>\n | Outcome from Spinner 1<\/td>\n | Outcome for Spinner 2<\/td>\n | Points (see Problem 4)<\/td>\n<\/tr>\n | \n| 1<\/td>\n | 3<\/td>\n | 3<\/td>\n | 4<\/td>\n<\/tr>\n | \n| 2<\/td>\n | 3<\/td>\n | 6<\/td>\n | 5<\/td>\n<\/tr>\n | \n| 3<\/td>\n | 1<\/td>\n | 5<\/td>\n | 4<\/td>\n<\/tr>\n | \n| 4<\/td>\n | 3<\/td>\n | 1<\/td>\n | 4<\/td>\n<\/tr>\n | \n| 5<\/td>\n | 2<\/td>\n | 4<\/td>\n | 5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Final Score: 22 Points<\/p>\n Player: Scott<\/p>\n \n\n\n| Trial<\/td>\n | Outcome from Spinner 1<\/td>\n | Outcome for Spinner 2<\/td>\n | Points (see Problem 4)<\/td>\n<\/tr>\n | \n| 1<\/td>\n | 2<\/td>\n | 2<\/td>\n | 5<\/td>\n<\/tr>\n | \n| 2<\/td>\n | 1<\/td>\n | 1<\/td>\n | 4<\/td>\n<\/tr>\n | \n| 3<\/td>\n | 1<\/td>\n | 4<\/td>\n | 5<\/td>\n<\/tr>\n | \n| 4<\/td>\n | 3<\/td>\n | 3<\/td>\n | 4<\/td>\n<\/tr>\n | \n| 5<\/td>\n | 2<\/td>\n | 2<\/td>\n | 5<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Final Score: 23 Points<\/p>\n Question 6.
\nAlan also included a fair coin as one of the scenario tools. Develop a scenario card (Scenario Card 3) that uses the coin and one of the spinners, include a description of the chance experiment and descriptions of five events
\nrelevant to the chance experiment.
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Algebra-2-Module-4-Lesson-1-Problem-Set-Answer-Key-1.png\")
\nAnswer:
\nAnswers will vary. Encourage students to be creative with this part of their assignment. Anticipate language similar to that used in the examples. A sample response card is included.<\/p>\n The following is an example of a completed Scenario Card 3:
\n![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Algebra-2-Module-4-Lesson-1-Problem-Set-Answer-Key-2.png\") <\/p>\n Question 7.
\nDetermine the sample space for your chance experiment. Then, complete the table below for the five events on your scenario card. Assign the numbers 1 – 5 to the descriptions you created.<\/p>\n \n\n\n| Event<\/td>\n | Outcomes<\/td>\n | \n Probability<\/p>\n<\/td>\n<\/tr>\n | \n| <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Answer:
\nEvaluate this chart based on the sample space and the descriptions developed by students. To evaluate, encourage
\nseveral students to explain their game scenario cards to other students, or provide a sample of the scenario cards
\ndeveloped for students to try. The sample response is based on the scenario card presented in Problem 6.<\/p>\n ![\"Eureka](\"https:\/\/ccssanswers.com\/wp-content\/uploads\/2021\/04\/Eureka-Math-Algebra-2-Module-4-Lesson-1-Problem-Set-Answer-Key-4.png\") <\/p>\n
Question 8.
\nDetermine a final score for your game based on five turns.<\/p>\n \n\n\n| Turn<\/td>\n | <\/td>\n | <\/td>\n | Points<\/td>\n<\/tr>\n | \n| <\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| <\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| <\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| <\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n | \n| <\/td>\n | <\/td>\n | <\/td>\n | <\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Answer:
\nAnswers vary based on the descriptions developed by students. Note: If time permits, encourage selected students to explain their games to other members of the class.<\/p>\n Eureka Math Algebra 2 Module 4 Lesson 1 Exit Ticket Answer Key<\/h3>\nQuestion 1.
\nFor the chance experiment described in Scenario Card 1, why is the probability of the event \u201cspinning an odd number and randomly selecting a blue card\u201d not the same as the probability of the event \u201cspinning an even number and randomly selecting a blue card\u201d? Which event would have the greater probability of occurring, and why?
\nAnswer:
\nThe first event includes the following outcomes from the sample space: (1, Blue-A), (1, Blue-B), (1, Blue-C), (1, Blue-D), (3, Blue-A), (3, Blue-B), (3, Blue-C), (3, Blue-D). The second event includes the following outcomes: (2, Blue-A), (2, Blue-B), (2, Blue-C), (2, Blue-D).<\/p>\n Because the spinner has two sectors representing odd numbers and only one sector representing an even number, the numbers of outcomes in the two events are different. The probability of the first event is \\(\\frac{8}{18}\\) compared to the probability of \\(\\frac{4}{18}\\) for the second event.<\/p>\n Question 2.
\nWhy is the probability of the event \u201cspinning an odd number from Spinner 1 and randomly selecting a blue card\u201d not equal to the probability of \u201cspinning an odd number from Spinner 1 or randomly selecting a blue card\u201d?
\nAnswer:
\nThe outcomes for the first event must include both the odd number and a blue card or (1, Blue-A), (1, Blue-B), (1, Blue-C), (1, Blue-D), (3, Blue-A), (3,Blue-B), (3,Blue-C), and (3, Blue-D). The probability of that event would be \\(\\frac{8}{18}\\) which is approximately 0.444. The outcomes of the second event would include each of the above outcomes, but it would also include the outcomes of odd numbers from the spinner with a red card and even numbers with a blue card.<\/p>\n The outcomes for this event include (1, Blue-A), (1, Blue-B), (1, Blue-C), (1, Blue-D), (1, Red-E), (1, Red-F), (2, Blue-A), (2,Blue-B), (2, Blue-C), (2, Blue-D), (3,Blue-A), (3,Blue-B), (3,Blue-C), (3, Blue-D), (3, Red-E), and (3, Red-F) . The only outcomes not included would be red cards with an even number. The probability for this event is \\(\\frac{16}{18^{\\prime}}\\) which is approximately 0.889.<\/p>\n Question 3.
\nIf one of the red cards is changed to a blue card, what is the probability of the event \u201cspinning an odd number from Spinner 1 and randomly selecting a red card from the card bag\u201d?
\nAnswer:
\nChanging one red card to a blue card will result in five blue cards and one red card in the card bag. Each of the five blue cards could be paired with each odd number that is possible from the spinner (the number 1 or the number 3). There would be a total of ten outcomes for this event. The number of outcomes in the sample space, however, would not change. As a result, the probability of this event is \\(\\frac{10}{18^{\\prime}}\\) which is approximately 0.556.<\/p>\n","protected":false},"excerpt":{"rendered":" Engage NY Eureka Math Algebra 2 Module 4 Lesson 1 Answer Key Eureka Math Algebra 2 Module 4 Lesson 1 Exercise Answer Key Exploratory Challenge\/Exercises 1 – 13: Exercise 1. Would you change any of the assignments of 1 – 5 that Alan made? Explain your answer. Assign the numbers 1 – 5 to the … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/89432"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=89432"}],"version-history":[{"count":1,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/89432\/revisions"}],"predecessor-version":[{"id":136832,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/89432\/revisions\/136832"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=89432"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=89432"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=89432"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}} | | | | | | | | | | | | | | | | | |