Probability math question

Question

Suppose you pay $1 to play a game in which a pair of fair (6-sided) dice is rolled. If a sum of 6,7, or 8 comes up you win $5. If a 2 or 12 comes up you win $3. Otherwise you lose the dollar you paid to play the game. Calculate the expected value for the game.

is this game fair? If not, is it more favorable for the player or the house?

Answer 1

Of the 36 possible sums of two die, 16 of them add up to 6 7 or 8, 2 add up to 12, leaving 18 that add up to neither. From that we can form the following probability distribution table:

Sum Amount Won P(Event)

6, 7, 8 $5 16/36 = 0.44

2, 12 $3 2/36 = 0.056

Other -1$ 18/36 = 0.5

E(winning) = 0.44 * 5 + 0.0-56 * 3 + 0.5 * -1 = $1.86

This game is more favorable to the player.