Question

Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that

(i) all the five cards are spades?

(ii) only 3 cards are spades?

(iii) none is a spade?

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.

X has a binomial distribution with n = 5 and

(i) P (all five cards are spades) = P(X = 5)

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

(iii) P (none is a spade) = P(X = 0)