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?
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. $\fbox{\frac{5}{9}}$