Have you ever seen Tossing a Coin before Commencement of a Cricket Match? This is usually done in Matches and the Captain who predicts the Toss Correctly can choose on what his team could defend. It is the most common application of the Coin Toss Experiment. Tossing a Coin is quite useful as the Probability of obtaining Heads is as likely as Tail. There are only two outcomes when you flip a coin i.e. Head(H) and Tail(T).
However, if you Toss 2, 3, 4, or more coins than that at the same time the Probability is Different. Let us learn about the Coin Toss Probability Formula in detail in the later sections. You can check out Solved Examples on Tossing a Coin and their Probabilities here.
Tossing a Coin Probability
When Tossed a Coin you will have only two possible outcomes i.e. Head or Tail. However, you will not know which outcome you will get among Heads or Tails. Tossing a Coin is a Random Experiment and you do know the set of Outcomes but not the exact outcomes.
General Formula to Determine the Probability = \(\frac { No.\; of\; Favorable\; Outcomes }{ Total\; Number\; of\; Possible\; Outcomes } \)
On Tossing, we do have only two possible outcomes
Probability of getting Head = \(\frac { No.\;of \;Outcomes\; to\; get\; Head }{ Total\; Number\; of\; Possible\; Outcomes } \)
= \(\frac { 1 }{ 2 } \)
Probability of getting Tail = \(\frac { No.\; of\; Outcomes\; to\; get\; Tail }{ Total\; Number\; of\; Possible\; Outcomes } \)
= \(\frac { 1 }{ 2 } \)
How to Predict Heads or Tails?
- If a coin is fair or unbiased, i.e. no outcome is particularly preferred, then it is difficult to predict heads or tails. Both the outcomes are equally likely to show up.
- If a coin is unfair or biased, i.e. an outcome is preferred, then we can predict the outcome by choosing the side that has a higher probability.
- If the probability of a head showing up is greater than 1/2, then we can predict the next outcome as a head.
- If the probability of a tail showing up is greater than 1/2, then we can predict the next outcome as a tail.
Solved Examples on Coin Toss Probability
1. On tossing a coin twice, what is the probability of getting only one Head?
Solution:
On tossing a coin twice, the possible outcomes are {HH, TT, HT, TH}
Therefore, the total number of outcomes is 4
Getting only one Head includes {HT, TH}
Thus, the number of favorable outcomes is 2
Hence, the probability of getting exactly one head = Probability of Favorable Outcomes/Total Number of Outcomes
= \(\frac { 1 }{ 2 } \)
2. Three fair coins are tossed simultaneously. What is the probability of getting at least three tails?
Solution:
When 3 coins are tossed, the possible outcomes are {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}.
Thus, the total number of possible outcomes = 8
Getting at least 3 tails include the outcomes = {TTT}
No. of Favorable Outcomes = 1
Probability of getting at least three tails include = Probability of Favorable Outcomes/Total Number of Outcomes
= \(\frac { 1 }{ 8 } \)