Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.
According to the statement
we have given that the Bob rolls a composite number, he eats sweetened cereal. If he rolls a prime number, he eats unsweetened cereal.
and we have to find that the expected value of the difference between the number of days.
So, the total number of days in a year is 365 days.
Chance to get a prime number on a die = 3/6
Chance to get a prime number on a die = 1/2.
and chances to get a composite number = 2/6
chances to get a composite number = 1/3
and chances to get a 1 on a die = 1/6.
Then the expected value =
so, expected value = 365(1/6) + 365(1/3) + 365(1/2)
then after calculating
Expected value = 1+2+1
then the value become is 4
and by this way he eat 171 days sweet cereal and other days he eat unsweetened.
So, Bob eats a 171 days sweetened cereal and 194 days he eat unsweetened cereal.
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with its given value: