Question

A friend offers you the following game: You will roll 2 fair dice. If the sum of the two numbers obtained is 2,3,4,9,10,11,or 12 the friend will pay you $20. However, if the sum of the two numbers is 5, 6,7, or 8, you pay your friend $20. This friend points out to you that there are 7 winning numbers and 4 losing numbers. What is the expected value of this game? Is this a fair game to you?

Answer 1

-2.22

Answer 2

Supposed a certain game is fair and costs $7 if you lose and has a net payoff of $9 if you win. The only possible outcomes of the game are winning and losing.