Posted by Maddy on Tuesday, October 23, 2012 at 11:13pm.
There are 6 combinations for the first dice, and 6 combinations for the second dice, so the total number of possibilities is 36
There are only 4 ways to get a sum of 9: (4,5), (5,4), (3, 6), (6, 3)
There are only 3 ways to get 4: (2, 2), (1,3), (3,1)
There are only 5 ways to get 6: (1,5), (5,1), (2,4), (4,2), (3,3)
So there are 8 ways to get 4 or 6
There are 36-8-4 = 24 other possible ways to get another number
For the game to be fair, the sum of all the probabilities multiplied by the gain/loss for each of them should be 0:
-$9 *(4/36) + $11*(8/36) + x*(24/36) = 0
solve for x