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?
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 p = 1/4
(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)
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- Bernoulli Trials and Binomial Distribution