Explanation Approach: 1. Mathematical expectation If an event E has several outcomes with probabilities p 1 , p 2 , p 3 , ⋯ , p n , and if for each of these outcomes the amount that can be won is a 1 , a 2 , a 3 , ⋯ , a n , respectively, then the mathematical expectation (or expected value) of E is EXPECTATION = a 1 p 1 + a 2 p 2 + a 3 p 3 + ⋯ , a n p n , 2. Expectation with a cost of playing If there is a cost of playing a game, the cost of playing must be subtracted. EXPECTATION = (Amount to win)(probability of winning) − cost of playing 3. Fair game A game is said to be fair if the expected value is 0. If the expected value is positive then the game is in your favor, and if the expected value is negative, then the game is not in your favor. Calculation: To determine whether the collectibles should be purchased or not, determine the expected value of purchasing

13th Edition

ISBN: 9781305855588

Author: SMITH

Publisher: CENGAGE CO

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Chapter 13.2, Problem 50PS

To determine

Whether the collectibles should be purchased if the cost is $500 and in order to make the purchase the expected profit should be at least $200. The details of the probabilities of various possible incomes from reselling collectibles are shown in below table.

Income Probability

$1, 000 0.12

$800 0.38

$500 0.45

$200 0.05

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Chapter 13.2, Problem 49PS

Chapter 13.2, Problem 51PS

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Chapter 13 Solutions

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Solution Summary: The author explains how to determine whether collectibles should be purchased if the cost is 500 and the expected profit is at least 200.

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