Every day a certain bank calculates its average daily deposit for that calendar month up to and including that day. If on a randomly chosen day in June the sum of all deposits up to and including that day is a prime integer greater than 100, what is the probability that the average daily deposit up to and including that day contains fewer than 5 decimal places?
(A)
(B)
(C)
(D)
(E)
Choose the correct choice from the following
A) 1/10 B) 2/15 C) 4/15 D) 3/10 E) 11/30
average=p/d has less than 5 decimal places? Where p=prime&gt;100 and d is the chosen day.   If the chosen day, d, is NOT of a type 2^n5^m (where n and m are nonnegative integers) then average=p/d will not be a terminating decimal and thus will have more than 5 decimal places.   How many such days are there of a type 2n5m: 1, 2, 4, 5, 8, 10, 16, 20, 25 (1=2^0∗5^0, 2=2^2, 4=2^2, 5, 8=2^3, 10=2∗5, 16=2^4, 20=22∗5, 2^5=52), total of 9 such days (1st of June, 4th of June, ...).   Now, does p divided by any of these d′s have fewer than 5 decimal places? Yes, as p/d∗10,000=integer for any such d (10,000 is divisible by all these numbers: 1, 2, 4, 5, 8, 10, 16, 20, 25).   So, there are 9 such days out of 30 in June: P=9/30=3/10 .   Answer: 3/10.
<result>D</result>
Every day a certain bank calculates its average daily deposit for that calendar month up to and including that day. If on a randomly chosen day in June the sum of all deposits up to and including that day is a prime integer greater than 100, what is the probability that the average daily deposit up to and including that day contains fewer than 5 decimal places?
(A)
(B)
(C)
(D)
(E)