4-31. You are gambling on a chess tournament with three matches taking place: 4 Probability and Counting 4.5 Exercises A

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4 31 You Are Gambling On A Chess Tournament With Three Matches Taking Place 4 Probability And Counting 4 5 Exercises A 1 (140.61 KiB) Viewed 37 times

4-31. You are gambling on a chess tournament with three matches taking place: 4 Probability and Counting 4.5 Exercises All players are equally matched, so the probability of any player winning a match is 1/2. You must guess which player will win each match. It costs you $10 to play, with prizes as follows: - Your original $10 back, plus an additional $20 if you guess all three matches correctly. - Your original $10 back if you guess exactly two of the matches correctly. - An amount of $2 if you guess a single match correctly. (a) Let X be the value of your winnings, so that X=0 corresponds to breaking even, a negative value of X corresponds to losing money, and a positive value of X means you win money. What is the expected value of X ? (b) You bribe Tyler to deliberately lose his match, guaranteeing that Parker will win. Assuming you pick Parker to win, what is the expected value of your winnings now?