A pair of fair dice is rolled once. suppose that you lose $ 8 if the dice sum to 3 and win $ 13 if the dice sum to 10 or 12. how much should you win or lo
Mathematics
rachelmkberg9867
Question
A pair of fair dice is rolled once. suppose that you lose $ 8 if the dice sum to 3 and win $ 13 if the dice sum to 10 or 12. how much should you win or lose if any other number turns up in order for the game to be fair?
1 Answer

1. User Answers MsEHolt
You should lose $1.20 for any other outcome to make it a fair game.
There are 2 ways to get a sum of 3 out of 36 outcomes; this probability is 2/36.
There are 4 ways to get a sum of 10 or 12 out of 36 outcomes; this probability is 4/36.
There are 36(2+4) = 366 = 30 other outcomes out of 36; this probability is 30/36.
We lose $8 if we get a sum of 3; this expected value is 8(2/36) = 16/36.
We win $13 if we get a sum of 10 or 12; this expected value is 13(4/36) = 52/36.
Using x as the amount we win or lose for the other outcomes, the expected value is 30x/36.
In order to be a fair game, the amount we win and/or lose should come outto( $0 total.
Together we have the equation
16/36+52/36+30x/36 = 0
Adding the fractions, we have
(16+52+30x)/36 = 0
(30x+36)/36 = 0
Multiplying both sides by 36,
30x+36=0*36
30x+36=0
Subtracting 36 from both sides,
30x+3636=036
30x=36
Dividing both sides by 30,
30x/30 = 36/30
x=36/30 = 1.2
Thus we should lose $1.20 for any other roll.