Explanation Given: A game in which $100 is offered if 3 cards are drawn from a standard deck of 52 cards and all cards are clubs. Explanation: Note that $100 is offered if 3 cards are drawn from a standard deck of 52 cards and all cards are clubs. Assume that $ x should be paid for the game, if the given game is a fair game. So, the payback for getting all 3 cards as clubs is $ ( 100 − x ) , and the payback for not getting all 3 cards as clubs is − $ x . The probability that all 3 clubs are drawn when 3 cards are drawn from a standard deck of 52 cards is P ( x = 3 ) = C ( 13 , 3 ) × C ( 39 , 0 ) C ( 52 , 3 ) = 286 × 1 22 , 100 = 0.01294 The probability that all 3 clubs are not drawn when 3 cards are drawn from a standard deck of 52 cards is P ( x ≠ 3 ) = 1 − 0.01294 = 0.98706 As the given game is a fair game, the expected value of the given game will be nonnegative

11th Edition

ISBN: 9780321979438

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

Publisher: PEARSON

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Chapter 8, Problem 48RE

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The amount that should be paid for the chance to win if the given game is a fair game.

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The amount that should be paid for the chance to win if the given game is a fair game.

Solution Summary: The author explains that 100 is offered if 3 cards are drawn from a standard deck of 52 cards. The expected value of the given game will be nonnegative.

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