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# Coin Toss Probability

Let us now look into the probability of tossing a coin. Quite often in games like cricket, for making a decision as to who would bowl or bat first, we sometimes use the tossing of a coin and decide based on the outcome of the toss. Let us check as to how we can use the concept of probability in the tossing of a single coin. Further, we shall also look into the tossing of two and three coming respectively.

### Tossing a Coin

A single coin on tossing has two outcomes, a head, and a tail. The concept of probability which is the ratio of favorable outcomes to the total number of outcomes can be used to find the probability of getting the head and the probability of getting a tail.

Total number of possible outcomes = 2; Sample Space = {H, T}; H: Head, T: Tail

• P(H) = Number of heads/Total outcomes = 1/2
• P(T)= Number of Tails/ Total outcomes = 1/2

### Tossing Two Coins

In the process of tossing two coins, we have a total of four outcomes. The probability formula can be used to find the probability of two heads, one head, no head, and a similar probability can be calculated for the number of tails. The probability calculations for the two heads are as follows.

Total number of outcomes = 4; Sample Space = {(H, H), (H, T), (T, H), (T, T)}

• P(2H) = P(0 T) = Number of outcome with two heads/Total Outcomes = 1/4
• P(1H) = P(1T) = Number of outcomes with only one head/Total Outcomes = 2/4 = 1/2
• P(0H) = (2T) = Number of outcome with two heads/Total Outcomes = 1/4

### Tossing Three Coins

The number of total outcomes on tossing three coins simultaneously is equal to 23 = 8. For these outcomes, we can find the probability of getting one head, two heads, three heads, and no head. A similar probability can also be calculated for the number of tails.

Total number of outcomes = 23 = 8 Sample Space = {(H, H, H), (H, H, T), (H, T, H), (T, H, H), (T, T, H), (T, H, T), (H, T, T), (T, T, T)}

• P(0H) = P(3T) = Number of outcomes with no heads/Total Outcomes = 1/8
• P(1H) = P(2T) = Number of Outcomes with one head/Total Outcomes = 3/8
• P(2H) = P(1T) = Number of outcomes with two heads /Total Outcomes = 3/8
• P(3H) = P(0T) = Number of outcomes with three heads/Total Outcomes = 1/8