Coin Toss Probability Formula

Before learning the coin toss probability formula, let us explore a few things about tossing a coin. The action of tossing a coin has two possible outcomes: Head or Tail. We don’t know which outcome we will obtain on a particular toss, but we do know that it will be either Head or Tail (we rule out the possibility of the coin landing on its edge!). However, tossing a coin is a random experiment, as you do know the set of outcomes, but you do not know the exact outcome for a particular execution of the random experiment. The coin toss probability formula helps in calculating the probability for any such experiment.

What Are Coin Toss Probability Formulas?

The probability of an event is defined as the ratio of the number of favorable outcomes to the total number of outcomes. The same applies to the coin toss probability formula as well.

Probability = Number of favorable outcomes/Total number of outcomes

When a coin is tossed, there are only two possible outcomes. Therefore, using the probability formula:

• On tossing a coin, the probability of getting head is:
  P(Head) = P(H) = 1/2

• Similarly, on tossing a coin, the probability of getting a tail is:
  P(Tail) = P(T) = 1/2

Let us see the applications of coin toss probability formulas in the following solved examples section.

Solved Examples Using Coin Toss Probability Formulas

Example 1: Coin-A is tossed 100 times, and the relative occurrence of Tails is 0.5. Coin-B is tossed an unknown number of times, but it is known that the relative occurrence of Heads is 0.48. Which coin is fairer?

Solution:  

To find: Fairer coin 

Given: For coin A:

Total number of outcomes for coin = 100

Relative Occurrence of tails = 0.5

For coin B:

Total number of outcomes for coin = unknown

Relative Occurrence of tails = 0.48

It is not possible to comment on the fairness of Coin-B, because the number of times it was tossed is not known.

On the other hand, Coin-A seems to be fair, as the relative occurrence of tails over a large number of tosses is almost 1/2.

Answer: It cannot be commented on which is a fairer coin based on given information.

Example 2: On tossing a coin twice, what is the probability of getting only one tail?

Solution:       

To find: the probability of getting only one tail

On tossing a coin twice, the possible outcomes are {HH, TT, HT, TH}

Therefore, the total number of outcomes is 4

Getting only one tail includes {HT, TH}

Therefore, the number of favorable outcomes is 2

Hence, using the coin toss probability formula,

the probability of getting exactly one tail is 2/4 = 1/2

Answer: The probability of getting exactly one tail = 1/2.