binomial probability

Question

Consider a card selected at a random and replaced. If this experiment is repeated 5 times, let us find the probability of selecting exactly 3 hearts. Use the binomial distribution. Also find out the mean and variance of binomial distribution.

Answer 1

Formula for probability of x successes in n tries with probability p of success in an individual try:

n!

---- p^x (1-p)^(n-x)

x! (n-x)!

Here n = 5, x = 3 and since there are 13 hearts in a 52 card deck, p = 13/52 = 1/4. Plug values into formula and compute.

mean = n * p = 5 * 1/4 = 1.25

variance = n * p * (1-p) = 5 * 1/4 * 3/4 = .0.9375