Explain why the experiment of tossing a coin three times

Question:
Explain why the experiment of tossing a coin three times is said to have binomial distribution.

Solution:

As the random variable X takes 0, 1, 2, 3, …, n is said to be binomial distribution having parameters n and p, if the probability is given by

P(X = r) = nCr pr qn-r, where q = 1 – p and r = 0, 1, 2, 3, …

Similarly, in case of tossing a coin 3 times, we have

n = 3 and X has the values 0, 1, 2, 3 with p = ½, q = ½.

Therefore, it is said that the experiment of tossing a coin three times have binomial distribution.