https://artofproblemsolving.com/wiki/api.php?action=feedcontributions&user=Nerdy19&feedformat=atom AoPS Wiki - User contributions [en] 2022-01-23T17:43:18Z User contributions MediaWiki 1.31.1 https://artofproblemsolving.com/wiki/index.php?title=2019_AMC_8_Problems/Problem_15&diff=144426 2019 AMC 8 Problems/Problem 15 2021-02-01T20:14:58Z <p>Nerdy19: /* Problem 15 */</p> <hr /> <div>==Problem 15==<br /> On a beach &lt;math&gt;50&lt;/math&gt; people are wearing sunglasses and &lt;math&gt;35&lt;/math&gt; 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 &lt;math&gt;\frac{2}{5}&lt;/math&gt;. If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap?<br /> &lt;math&gt;\textbf{(A) }\frac{14}{85}\qquad\textbf{(B) }\frac{7}{25}\qquad\textbf{(C) }\frac{2}{5}\qquad\textbf{(D) }\frac{4}{7}\qquad\textbf{(E) }\frac{7}{10}&lt;/math&gt;<br /> <br /> ==Video Solution==<br /> https://youtu.be/6xNkyDgIhEE?t=252<br /> <br /> ==Solution 1==<br /> The number of people wearing caps and sunglasses is <br /> &lt;math&gt;\frac{2}{5}\cdot35=14&lt;/math&gt;. So then 14 people out of the 50 people wearing sunglasses also have caps. <br /> &lt;math&gt;\frac{14}{50}=\boxed{\textbf{(B)}\frac{7}{25}}&lt;/math&gt;<br /> <br /> ==Video Solution==<br /> https://www.youtube.com/watch?v=gKlYlAiBzrs ~ MathEx<br /> <br /> Another video - https://www.youtube.com/watch?v=afMsUqER13c<br /> <br /> https://youtu.be/37UWNaltvQo -Happytwin<br /> <br /> ==See Also==<br /> {{AMC8 box|year=2019|num-b=14|num-a=16}}<br /> <br /> {{MAA Notice}}</div> Nerdy19