2011 AMC 12B Problems/Problem 9

Problem

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?

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

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 $\frac{1}{3}*\frac{1}{2}=\frac{1}{9}$ chance.

Therefore, the total probability is $\frac{4}{9}+\frac{1}{9}=\frac{5}{9}$ and we are done. $\boxed{D}$

2011 AMC 12B (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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2011 AMC 12B Problems/Problem 9

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