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Three standard fair 6-sided dice are rolled. What is the expected number of 6's rolled? (For example, if two 6's and a 5 are rolled, then the answer is 2.)

 Jan 2, 2023
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The expected value of the number of sixes is all the number of cases for the number of sixes * probability to get that number of 6s, all added together. 

The probability to get three sixes is (1/6)^3=1/216 

The probability to get two sixes is (1/6)*(1/6)*(5/6)*3 = 15/216

The probability to get one six is (1/6)*(5/6)*(5/6)*3 = 75/216

The expected value of sixes is 3*1/216 + 2*15/216 + 1*75/216 = 3/216 + 30/216 + 75/216 = 108/216 = 1/2

 Jan 2, 2023

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