1. Consider a game played by rolling a set of three 3-sided dice one time and adding the values from the dice together to form a sum. The game costs $7 to play once. You don't get any prize for rolling a sum of 5 or 7, you get $12 for a sum of 4 or 8, and you get $37 for a sum of 3 or 9. If the game is "fair," what is the prize for rolling a 6? (Hint: form a probability distribution to help you find the missing value and recall what "expected value" means in the context of a probability distribution.)

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1. Consider a game played by rolling a set of three 3-sided dice one time and
adding the values from the dice together to form a sum. The game costs $7 to
play once. You don't get any prize for rolling a sum of 5 or 7, you get $12 for a
sum of 4 or 8, and you get $37 for a sum of 3 or 9. If the game is "fair," what is
the prize for rolling a 6? (Hint: form a probability distribution to help you find
the missing value and recall what "expected value" means in the context of a
probability distribution.)
Transcribed Image Text:1. Consider a game played by rolling a set of three 3-sided dice one time and adding the values from the dice together to form a sum. The game costs $7 to play once. You don't get any prize for rolling a sum of 5 or 7, you get $12 for a sum of 4 or 8, and you get $37 for a sum of 3 or 9. If the game is "fair," what is the prize for rolling a 6? (Hint: form a probability distribution to help you find the missing value and recall what "expected value" means in the context of a probability distribution.)
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