MathDB
Sunglasses and Caps

Source: 2019 AMC 8 #15

November 19, 2019

Problem Statement

On a beach 50 people are wearing sunglasses and 35 people are wearing caps. Some people are wearing both sunglasses and caps. If one of the people wearing a cap is selected at random, the probability that this person is also wearing sunglasses is 25\frac{2}{5}. If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap?
<spanclass=′latex−bold′>(A)</span>1485<spanclass=′latex−bold′>(B)</span>725<spanclass=′latex−bold′>(C)</span>25<spanclass=′latex−bold′>(D)</span>47<spanclass=′latex−bold′>(E)</span>710<span class='latex-bold'>(A) </span>\frac{14}{85}\qquad<span class='latex-bold'>(B) </span>\frac{7}{25}\qquad<span class='latex-bold'>(C) </span>\frac{2}{5}\qquad<span class='latex-bold'>(D) </span>\frac{4}{7}\qquad<span class='latex-bold'>(E) </span>\frac{7}{10}
Back to ProblemsView on AoPS