Question

What is probability of getting 4 heads in un biased coin?

Answer 1

Let X represent the number of coin flips that result in getting a head. Since we have a fair coin and there are 8 coin flips, X follows a Binomial Distribution with n = 8 and p = 0.5. The probability mass function for a Binomial random variable is the following:

P(X = x) = (nx)pxqn−x

where n is the number of trial, x is the number of successes, p is the probability of success and q is the probability of failure (where q = 1 - p).

With this problem, n = 8, x = 4, p = 0.5 and q = 0.5 and so we have

P(X = 4) = (84)(0.5)4(0.5)4

=0.2734.

Thus the probability of getting 4 heads in 8 coin flips is 0.2734.

You can calculate this in R using the dbinom() function as follows:

dbinom(x = 4,size = 8,prob = .5)
and you get the same answer.