Problem:
Twelve fair dice are rolled. What is the probability that the product of the numbers on the top faces is prime?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Exactly one die must have a prime face on top, and the other eleven must have 's. The prime die can be any one of the twelve, and the prime can be , or . Thus the probability of a prime face on any one die is , and the probability of a prime product is
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions