If a gambler rolls 2 dice and gets a sum of 4 he wins 10 dol

If a gambler rolls 2 dice and gets a sum of 4 he wins 10 dollars and if he gets a sum of 3 he wins 25 dollars. the cost to play the game is 5 dollars. what is the expectiation of this game?

Solution

Sum        :    3       4 neither 3 nor 5

Amount    : (25-5)=20     (10-5)=5                -5

Probabilities :     2/36            3/36             31/36

Eexpectation of amount = E(X) = 20*(2/36) + 5*(3/36)    +    -5*(31/36)    = -100/36 = -2.77 dollars