AMC12 2011 12B, Problem 9

Two real numbers are selected independently and at random from the interval $[-20,10]$.  What is the probability that the product of those numbers is greater than zero?

Solution: For the product to be greater than zero, we must have either both numbers negative or both positive. Both numbers are negative with a $\frac{2}{3}*\frac{2}{3}=\frac{4}{9}$ chance. Both numbers are positive with a $\frac{1}{3}*\frac{1}{3}=\frac{1}{9}$ chance. Therefore, the total probability is $\frac{4}{9}+\frac{1}{9}=\frac{5}{9}$ and we are done. $\fbox{\frac{5}{9}}$

Answer: \frac{5}{9}