Problem:
Two eight-sided dice each have faces numbered through . When the dice are rolled, each face has an equal probability of appearing on the top. What is the probability that the product of the two top numbers is greater than their sum?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are ordered pairs that can represent the top numbers on the two dice. Let and represent the top numbers on the dice. Then implies that , that is,
This inequality is satis ed except when , or when . There are ordered pairs excluded by these conditions, so the probability that the product is greater than the sum is
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions