Question

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 value of the difference between the number of days Bob eats unsweetened cereal and the number of days he eats sweetened cereal?

Answer 1

what about 1?

Answer 2

oh he rolls again

Answer 3

primes are 2, 3, 5, composite 4, 6, so he gets prime \(\frac{3}{5}\) of the time, composite \(\frac{2}{5}\) of the time

Answer 4

\[\frac{3}{5}\times 365-\frac{2}{5}\times 365\] will give you the expected value of the difference

Answer 5

Thanks