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?

Answer 1

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