+1836 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?
+23252 2, 3, and 5 are prime numbers; 4 and 6 are composite.
Therefore, (approximately) 60% of the time, he will roll a prime number and 40% of the time he will roll a composite number.
60% of 365 is 219; 40% of 365 is 146.
219 - 146 = 73 days.
It is expected that he will eat unsweetened cereal 73 more days than he eats sweetened cereal in a year.
+23252 2, 3, and 5 are prime numbers; 4 and 6 are composite.
Therefore, (approximately) 60% of the time, he will roll a prime number and 40% of the time he will roll a composite number.
60% of 365 is 219; 40% of 365 is 146.
219 - 146 = 73 days.
It is expected that he will eat unsweetened cereal 73 more days than he eats sweetened cereal in a year.
