Question

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards, find the probability that only 3 cards are spades.

Answer 1

Let X represent the number of spade cards among the five cards drawn. Since the drawing of card is with replacement, the trials are Bernoulli trials.

In a well shuffled deck of 52 cards, there are 13 spade cards.

\(p = \frac{13}{52} = \frac{1}{4}\)

\(q = 1 - \frac{1}{4} = \frac{3}{4}\)

X has a binomial distribution with n = 5 and p = 1/4

P (only 3 cards are spades) = P(X = 3)