Problem:
Two real numbers are selected independently at random from the interval . What is the probability that the product of those numbers is greater than zero?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Consider all ordered pairs with each of the numbers and in the closed interval . These pairs fill a square in the coordinate plane, with an area of 900 square units. Ordered pairs in the first and third quadrants have the desired property, namely . The areas of the portions of the square in the first and third quadrants are and , respectively. Therefore the probability of a positive product is .
\section*{OR}
Each of the numbers is positive with probability and negative with probability . Their product is positive if and only if both numbers are positive or both are negative, so the requested probability is .
The problems on this page are the property of the MAA's American Mathematics Competitions