Consider a standard deck of poker cards Suppose 4 cards are

Consider a standard deck of poker cards. Suppose 4 cards are drawn at random from the deck without replacement. What is the probability that at most 3 cards are red?

Solution

a standard deck of poker cards are 52 , among 26 are red, 26 are black.

drawn 4 cards from a standard deck is 52 C 4

number of possibiliies at most 3 cards are red among 4 drawn are = 1 drawn from red * 3 from black + 2 are from red * 2 are from black + 3 are from red * 1 is from black = 26 C 1 * 26 C 3 + 26 C 2 * 26 C 2 + 26 C 3 * 26 C 1

Probability of at most 3 cards are red= ( 26 C 3 * 26 C 1 + 26 C 4 ) / 52 C 4 = (nCr(26,3)nCr(26,1)+nCr(26,2)*nCr(26,2)+nCr(26,3)nCr(26,1))/nCr(52,4) = 0.8895