2019 AMC 8 Problems/Problem 15
Contents
Problem 15
On a beach people are wearing sunglasses and 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 . If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap?
Solution 1
The number of people wearing caps and sunglasses is . So then, 14 people out of the 50 people wearing sunglasses also have caps.
Solution 2
Let be the event that a randomly selected person is wearing sunglasses, and let be the event that a randomly selected person is wearing a cap. We can write in two ways: or . Suppose there are people in total. Then and Additionally, we know that the probability that someone is wearing sunglasses given that they wear a cap is , so . We let , which is the quantity we want to find, be equal to . Substituting in, we get
Note: This solution makes use of the dependent events probability formula, , where represents the probability that occurs given that has already occurred and represents the probability of both and happening.
~ cxsmi
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
-Happytwin
Video Solution
Solution detailing how to solve the problem: https://www.youtube.com/watch?v=omRgmX7KXOg&list=PLbhMrFqoXXwmwbk2CWeYOYPRbGtmdPUhL&index=16
Video Solution
~savannahsolver
Video Solution (MOST EFFICIENT+ CREATIVE THINKING!!!)
~Education, the Study of Everything
Video Solution by The Power of Logic(Problem 1 to 25 Full Solution)
~Hayabusa1
See Also
2019 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 14 |
Followed by Problem 16 | |
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