Explanation Given: A game where a die is rolled with different payoffs for different outcomes Explanation: Consider the game given in the textbook. $6 are paid to play in the game where a die is rolled. Different payoffs are as follows: $8 for a 6, $7 for a 5, and $4 for any other result The sample space for rolling a die is S = { 1 , 2, 3, 4, 5, 6 } So, the number of elements in the sample space is n ( S ) = 6 . Here, the random variable represents the possible amounts of payback, where payback equals the amount won minus the cost to play the game. The payback for getting a 6 is $ 8 − $ 6 = $ 2 The payback for getting a 5 is $ 7 − $ 6 = $ 1 . The payback for getting any other number (from 1 to 4) is $ 4 − $ 6 = − $ 2 . The probability distribution for given experiment is as follows: x $ 2 $ 1 − $ 2 p ( x ) 1 6 1 6 4 6 Use the formula for the expected value of a random variable: E ( x ) = x 1 p 1 + x 2

11th Edition

ISBN: 9780321979438

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

Publisher: PEARSON

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Chapter 8, Problem 45RE

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The expected winnings in the given game where a die is rolled and determine whether it is a fair game or not.

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Chapter 8, Problem 44RE

Chapter 8, Problem 46RE

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The expected winnings in the given game where a die is rolled and determine whether it is a fair game or not.

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The expected winnings in the given game where a die is rolled and determine whether it is a fair game or not.

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