Difference between revisions of "2019 AMC 8 Problems/Problem 15"
Aggarwalr123 (talk | contribs) m (→Video Solution) |
|||
| (14 intermediate revisions by 8 users not shown) | |||
| Line 1: | Line 1: | ||
==Problem 15== | ==Problem 15== | ||
| − | On a beach <math>50</math> people are wearing sunglasses and <math>35</math> 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 <math>\frac{2}{5}</math>. If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap? | + | On a beach <math>50</math> people are wearing sunglasses and <math>35</math> 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 <math>\frac{2}{5}</math>. If instead, someone wearing sunglasses is selected at random, what is the probability that this person is also wearing a cap? |
| + | |||
<math>\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}</math> | <math>\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}</math> | ||
| − | |||
| − | |||
| − | |||
==Solution 1== | ==Solution 1== | ||
The number of people wearing caps and sunglasses is | The number of people wearing caps and sunglasses is | ||
| − | <math>\frac{2}{5}\cdot35=14</math>. So then 14 people out of the 50 people wearing sunglasses also have caps. | + | <math>\frac{2}{5}\cdot35=14</math>. So then, 14 people out of the 50 people wearing sunglasses also have caps. |
| + | |||
<math>\frac{14}{50}=\boxed{\textbf{(B)}\frac{7}{25}}</math> | <math>\frac{14}{50}=\boxed{\textbf{(B)}\frac{7}{25}}</math> | ||
| − | ==Solution Explained== | + | ==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 | https://youtu.be/gOZOCFNXMhE ~ The Learning Royal | ||
| − | ==Video Solution== | + | ===Video Solution by OmegaLearn=== |
| − | https://www.youtube.com/watch?v=gKlYlAiBzrs ~ MathEx | + | 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 | |
| − | == Video Solution == | + | 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 | 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== | ==See Also== | ||
Latest revision as of 16:17, 30 December 2023
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.
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 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
| All AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
