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Beth rolls a fair six-sided die. If she rolls a prime number, she wins 1 dollar, but if she rolls a composite number, she loses 1 dollar. If she rolls 1 nothing happens. What is the expected value of the amount of money Beth will win if she rolls the die once? Express your answer as a common fraction.

 Dec 20, 2020
 #1
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By linearity of expectation, the expected value is 4/5 of a dollar.

 Dec 21, 2020
 #2
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Expected win = (0 + 1 + 1 - 1 + 1 - 1)/6 = $1/6

 Dec 21, 2020

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