Five cards are drawn at random with replacement from a deck of 52 cards. What is the probability of getting four spades?

Solution

Here n = 5
p = P(spade) = $13 over 52 space equals 1 fourth comma space space straight q space equals space 1 space minus space straight p space equals space 1 space minus 1 fourth space equals space 3 over 4$
P(4 spades) = $straight P left parenthesis 4 right parenthesis space equals space straight C presuperscript 5 subscript 4 space open parentheses 3 over 4 close parentheses to the power of 5 minus 4 end exponent space open parentheses 1 fourth close parentheses to the power of 4 space equals space 5 over 1 cross times 3 over 4 cross times 1 over 256 space equals 15 over 1024$

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Probability

Five cards are drawn at random with replacement from a deck of 52 cards. What is the probability of getting four spades?

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