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Bob rolls a fair six-sided die each morning. If Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal. If he rolls a 1, then he rolls again. In a non-leap year, what is the expected number of times Bob will roll his die?

 Mar 31, 2019
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On any one day Bob will expect to roll once 5/6 of the time, twice 5/62 of the time, three times 5/63 of the time, ...etc.

 

Expected number for one day = 1*5/6 + 2*5/62 + 3*5/63 + ...  = 6/5

 

Expected number for a non-leap year = 365*6/5 = 438

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 Apr 1, 2019

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