Question

At this years 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. If the cost is $3 to play one game with one roll of the dice. What is the expectation of the game?

Answer 1

Expectation of the gain;

E = (2×$17 + 6×$2 - 28×3)/36

E = -$1.06

Explanation:

For 2 and 12

Number of possible outcomes = 2

Gain = 20 - 3 = $17

For 7

Number of possible outcomes = 6

Gain = 5-3 = $2

For others

Number of possible outcomes = 36-(2+6) = 28

Gain = -$3

Expectation of the gain;

E = (2×$17 + 6×$2 - 28×3)/36 = -$38/36

E = -$1.06