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An ordinary deck of 52 cards is shuffled. What is the probability th.pdf

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An ordinary deck of 52 cards is shuffled. What is the probability that the top four cardshave (a) different denominations? (b) different suits? Solution a) P(diff deno)=(52*48*44*40)/(52*51*50*49)=0.6761 b) There are 24 different ways to get 4 cards of different suits (H,S,C,D or H,S,D,C, or H,C,S,D...). Each combination is equally likely, so we’ll find the probability of one of them, and then multiply it by 24 to get the answer. The probability of H,S,C,D is (13/52) * (13/51) * (13/50) * (13/49) = 0.0044. So multiply by 24 to get 0.105.

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An ordinary deck of 52 cards is shuffled. What is the probability that the top four cardshave (a) different denominations? (b) different suits? Solution a) P(diff deno)=(52*48*44*40)/(52*51*50*49)=0.6761 b) There are 24 different ways to get 4 cards of different suits (H,S,C,D or H,S,D,C, or H,C,S,D...). Each combination is equally likely, so we’ll find the probability of one of them, and then multiply it by 24 to get the answer. The probability of H,S,C,D is (13/52) * (13/51) * (13/50) * (13/49) = 0.0044. So multiply by 24 to get 0.105

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  • 1. An ordinary deck of 52 cards is shuffled. What is the probability that the top four cardshave (a) different denominations? (b) different suits? Solution a) P(diff deno)=(52*48*44*40)/(52*51*50*49)=0.6761 b) There are 24 different ways to get 4 cards of different suits (H,S,C,D or H,S,D,C, or H,C,S,D...). Each combination is equally likely, so we’ll find the probability of one of them, and then multiply it by 24 to get the answer. The probability of H,S,C,D is (13/52) * (13/51) * (13/50) * (13/49) = 0.0044. So multiply by 24 to get 0.105