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Probability that product is greater than zero

Source: AMC 10 2011 b Problem 13

February 24, 2011
probabilityratiogeometry3D geometrytetrahedronlimitcalculus

Problem Statement

Two real numbers are selected independently at random from the interval [-20, 10]. What is the probability that the product of those numbers is greater than zero?
<spanclass=′latex−bold′>(A)</span> 19<spanclass=′latex−bold′>(B)</span> 13<spanclass=′latex−bold′>(C)</span> 49<spanclass=′latex−bold′>(D)</span> 59<spanclass=′latex−bold′>(E)</span> 23 <span class='latex-bold'>(A)</span>\ \frac{1}{9} \qquad <span class='latex-bold'>(B)</span>\ \frac{1}{3} \qquad <span class='latex-bold'>(C)</span>\ \frac{4}{9} \qquad <span class='latex-bold'>(D)</span>\ \frac{5}{9} \qquad <span class='latex-bold'>(E)</span>\ \frac{2}{3}
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