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?

Question

Mathematics

Ayanna Chen

9 March, 05:17

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?

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Answers (1)

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Brogan Cline · Answer 1

Expectation of the gain;

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

E = - $1.06

Step-by-step 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