2019 AMC 8 Problems/Problem 15

Problem 15

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 $\frac{2}{5}$. If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap?

$\textbf{(A) }\frac{14}{85}\qquad\textbf{(B) }\frac{7}{25}\qquad\textbf{(C) }\frac{2}{5}\qquad\textbf{(D) }\frac{4}{7}\qquad\textbf{(E) }\frac{7}{10}$

Solution 1

The number of people wearing caps and sunglasses is $\frac{2}{5}\cdot35=14$. So then, 14 people out of the 50 people wearing sunglasses also have caps.

$\frac{14}{50}=\boxed{\textbf{(B)}\frac{7}{25}}$

Video Solutions

Video Solution by Math-X (First fully understand the problem!!!)

https://youtu.be/IgpayYB48C4?si=V_SNrrp17pztxbQG&t=4518

~Math-X

Solution Explained

https://youtu.be/gOZOCFNXMhE ~ The Learning Royal

Video Solution by OmegaLearn

https://youtu.be/6xNkyDgIhEE?t=252

~ pi_is_3.14

Video Solution

https://www.youtube.com/watch?v=gKlYlAiBzrs

~ MathEx

https://www.youtube.com/watch?v=afMsUqER13c

Another video

https://youtu.be/37UWNaltvQo

-Happytwin

Video Solution

Solution detailing how to solve the problem: https://www.youtube.com/watch?v=omRgmX7KXOg&list=PLbhMrFqoXXwmwbk2CWeYOYPRbGtmdPUhL&index=16

Video Solution

https://youtu.be/9nbaMSAQCNU

~savannahsolver

Video Solution (MOST EFFICIENT+ CREATIVE THINKING!!!)

https://youtu.be/cK_mfkZ_rYM

~Education, the Study of Everything

Video Solution by The Power of Logic(Problem 1 to 25 Full Solution)

https://youtu.be/Xm4ZGND9WoY

~Hayabusa1

See Also

2019 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 14
Followed by
Problem 16
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All AJHSME/AMC 8 Problems and Solutions

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