Problem:
Suppose and are single-digit positive integers chosen independently and at random. What is the probability that the point lies above the parabola ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The point is above the parabola if and only if . Because is positive, this is equivalent to . If , then can be any digit from 1 to 9 inclusive. If , then can be any digit between 3 and 9 inclusive. If , then can be any digit between 7 and 9 inclusive. If , there is no that satisfies . Therefore there are pairs satisfying the condition, out of a total of pairs. The requested probability is .
The problems on this page are the property of the MAA's American Mathematics Competitions