Problem:
Integers , and , not necessarily distinct, are chosen independently and at random from to , inclusive. What is the probability that is even?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The number is even if and only if and are both odd or are both even. Each of and is odd if both of its factors are odd, and even otherwise. Exactly half of the integers from to are odd, so each of and is odd with probability and are even with probability . Hence the probability that is even is
The problems on this page are the property of the MAA's American Mathematics Competitions