2017 AMC 12B Problems/Problem 10
Problem
At Typico High School, 
of the students like dancing, and the rest dislike it. Of those who like dancing, 
say that they like it, and the rest say that they dislike it. Of those who dislike dancing, 
say that they dislike it, and the rest say that they like it. What fraction of students who say they dislike dancing actually like it?
Solution 1
WLOG, let there be 
students. 
of them like dancing, and 
do not. Of those who like dancing, 
, or 
of them say they dislike dancing. Of those who dislike dancing, , or 
of them say they dislike it. Thus, 
Solution 2 (Bayes' Theorem)
The question can be translated into P(Likes|Says Dislike).
By Bayes' Theorem, this is equal to the probability of 
. 
, and 
.
Therefore, you get a probability of 
~Directrixxx
See Also
| 2017 AMC 12B (Problems • Answer Key • Resources) | |
| Preceded by Problem 9 |
Followed by Problem 11 |
| 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 AMC 12 Problems and Solutions | |
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