Answer to Question #331175 in Statistics and Probability for rosemae

Question

You play a game with two six-sided dice. If you roll a sum of 8, you win P800 and if you roll a sum of 6, you win P600. However, you lose P500 if you roll anything else. If you continue to play this game, how much do you expect to win lose or win in the game?

Answer 1

The total number of outcomes when rolling two dice is $N=6\cdot6=36.$

Five of them are favorable to getting a sum of 8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2).

Five other outcomes are favorable to getting a sum of 6: (1, 5), (2, 4), (3, 3), (4, 2), (5, 1).

The expected value of the game result:

$\mu=\sum x_ip_i=\\ =800\cdot\cfrac{5}{36}+600\cdot\cfrac{5}{36}+(-500)\cdot\cfrac{36-5-5}{36}=-166.67.$

So, I expect to lose P166.67.