Dice Winning - MATH 101

Question

In a dice game, you win if the two dice come up 10 or higher. Otherwise, you lose $1. What should be the profit for winning to make this game fair?

A $5

B $4 

C $7

D $6

Answer 1

{5,5} {6,4} {4,6}

{5,6} {6,5}

{6,6}

Prob(win) = 7/36

prob(loss) = 29/36

Let x be the winning amount

Expected value is X(7/36) + (-1)(29/36) = 0

(7/36)x - 29/36 = 0

(7/36)x = 29/36

7x = 29

x = 29/7 = 4 and 1/7

So $5 which is option A