Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Difference between revisions of "2019 AMC 8 Problems/Problem 15"

m (→‎Solution 1)
m (→‎Problem 15: added extra line between problem & ans choices to make formatting better on AMCTrivial)
 
(19 intermediate revisions by 13 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  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==
 +
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==
 
==See Also==

Latest revision as of 21:27, 26 October 2023

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.

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

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 (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. AMC logo.png

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2019_AMC_8_Problems/Problem_15&oldid=200324"