Asked by Preet

Bill and Fred are betting on the outcome when two fair dice are rolled. If the dice sum is any even number, other than 8, Bill pays Fred $8. If the dice sum is 8, Bill pays Fred $1. If the dice sum is odd, Fred pays Bill $2. What is Fred's expected payoff for this game?

Answers

Answered by Steve
P(even,~8) = P(2,4,6,10,12)
= 1/36 + 3/36 + 5/36 + 3/36 + 1/36 = 13/36
P(8) = 5/36
P(odd) = 1-(13/36 + 5/36) = 1/2

So, Fred gets 8*13/36 + 1*5/36 - 2*1/2 = 73/36, or about $2
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