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Unformatted text preview: Example 31. Bridge Hand with 13 cards In a bridge hand with 13 cards, what is the probability of getting 9 Hearts, 0 Clubs, 2Spades and 2 Diamonds? We will find the answer using conditional probability. By the definition of conditional probability, P(9H 0C 2S 2D)=P(9H)P(0C|9H)P(2S|9H 0C)P(2D|9H 0C 2S) A deck of 52 cards contains 13 cards of each suit. P(9H in a hand of 13) = P (9H and 4 non-hearts in a hand of 13) There are 13 hearts, 39 non-heart cards to choose from, hence: 13 39 9 4 (9 ) 52 13 P H ! "! " # $# $ % &% & = ! " # $ % & Now given that the hand contains 9 hearts, what is the probability that there are 0 clubs? Now we are concerned about the 4 non-heart cards. There are 39 4 ! " # $ % & ways of choosing 4 non-heart cards from 39 non-heart cards. Of these, there are 26 cards (13 Spades, 13 diamonds) that are not hearts and not clubs. So we need to choose 4 cards from these 26 cards ( 26 4 ! " # $ % & ways) and 0 cards from the remaining 13 clubs ( 13...
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- Spring '08