Explanation Given: 13 cards are dealt to each player from a deck of 52 cards in the card game. Explanation: Consider the experiment of dealing 13 cards to each player from a deck of 52 cards. The number of elements in the sample space will be equal to the number of ways of selecting 13 cards from 52 cards. That is, n ( S ) = C ( 52 , 13 ) = 52 ! 13 ! × ( 52 − 13 ) ! = 635 , 013 , 559 , 600 Assume that, E represents the event that the bridge hand contains at least 3 aces. As there are 4 aces, one from each suit in a deck of 52 cards, the event E consists of 3 aces and 4 aces. The number of ways of selecting 3 aces from four aces is C ( 4 , 3 ) and the number of ways of selecting 13 − 3 = 10 cards from remaining 52 − 4 = 48 non-ace cards is C ( 48 , 10 ) . So, the number of bridge hands with exactly 3 aces is, C ( 4 , 3 ) × C ( 48 , 10 ) The number of ways of selecting 4 aces from four aces is C ( 4 , 4 ) and the number of ways of selecting 13 − 3 = 9 cards from the remaining 52 − 4 = 48 non-ace cards is C ( 48 , 9 )

Finite Mathematics, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

11th Edition

ISBN: 9780133886818

Author: Margaret L. Lial, Raymond N. Greenwell, Nathan P. Ritchey

Publisher: PEARSON

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Chapter 8.3, Problem 56E

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The probability that a bridge hand contains at least 3 aces when 13 cards are dealt.

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The probability that a bridge hand contains at least 3 aces when 13 cards are dealt.

Solution Summary: The author analyzes the probability that a bridge hand contains at least 3 ace when 13 cards are dealt. The number of elements in the sample space will be equal to the amount of ways of selecting 13 from 52 cards.

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