Question

You are given 9 to 1 odds against rolling a sum of 8 with the roll of two fair dice, meaning you win $9 if you succeed and you lose $1 if you fail. Find the expected value (to you) of the game.

Answer 1

Given prob of not rolling 8 is 9/10
then prob of rolling 8 = 1/10

NOTE: with a roll of 2 fair dice, the above given probability is not correct,
prob(rolling an 8) is 5/36 and prob (not rolling a sum of 8 is 31/36

But, going with your data anyway, ....

expected value = (1/10)(9) - (9/10)(1) = 0

REAl expected value
= (5/36)(9) - (31/36)(1) = 19/9 or appr 2.11

Answer 2

actually it is 1.25-.86