Question

You roll a pair of dice. You bet $1 that you will get a 2,3, or 12. If you win, you are paid $9 (a profit of $8).

Show that this is a fair game.

Answer 1

the probability of getting 2,3, or 12 is 4/36, or 1/9, and the probability of NOT getting those numbers is 8/9

then, we calculate the expected value:

(1/9)(8) + (8/9)(-1) = 0, and since the expected value is 0, this is a fair game

Answer 2

@Vocaloid thank you for your help