A pair of fair dice is rolled once. Suppose that you lose $8 if the dice sum to 7 and win $12 if the dice sum to 10 or 6. How much should you win or lose if any other number turns up in order for the game to be fair?

Question

A pair of fair dice is rolled once. Suppose that you lose ​$8 if the dice sum to 7 and win ​$12 if the dice sum to 10 or 6. How much should you win or lose if any other number turns up in order for the game to be​ fair?

oobleck · Answer

figure the probabilities of the win/lose events. Then if
P1 = P(7)
P2 = P(6 or 10)
P3 = 1 - P1 - P2
Then the win/loss of $x needed to make the game fair (Expected value = 0) is
-8P1 + 12P2 + P3*x = 0
come on back if you have trouble with P1 or P2

A pair of fair dice is rolled once. Suppose that you lose ​$8 if the dice sum to 7 and win ​$12 if the dice sum to 10 or 6. How much should you win or lose if any other number turns up in order for the game to be​ fair?

A pair of fair dice is rolled once. Suppose that you lose $8 if the dice sum to 7 and win $12 if the dice sum to 10 or 6. How much should you win or lose if any other number turns up in order for the game to be fair?