At this year's State Fair, there was a dice rolling game. If you rolled two dice and got a sum of 2 or 12, you won $20. If you rolled a 7,you won $5. Any other roll was a loss. It cost $3 to play one game with one roll of the dice. What is the expectation of the game?

Answer 1

Calculate the product of the net gain (i.e. gain minus the bet of $3) and the probability of each outcome.
Add all the products to get the expectation of the game.
Note that the probabilities of all the outcomes must add up to exactly 1.0