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?
$\textbf{(A)}\ \frac{1}{9} \qquad \textbf{(B)}\ \frac{1}{3} \qquad \textbf{(C)}\ \frac{4}{9} \qquad \textbf{(D)}\ \frac{5}{9} \qquad \textbf{(E)}\ \frac{2}{3}$
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. $\boxed{D}$




[2011 AMC 12B](https://artofproblemsolving.com/wiki/index.php/2011_AMC_12B) ([Problems](https://artofproblemsolving.com/wiki/index.php/2011_AMC_12B_Problems) • [Answer Key](https://artofproblemsolving.com/wiki/index.php/2011_AMC_12B_Answer_Key) • [Resources](https://artofproblemsolving.comhttp://www.artofproblemsolving.com/community/c13))


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