Difference between revisions of "2017 AMC 12B Problems/Problem 10"
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==Solution 2- Bayes' Theorem== | ==Solution 2- Bayes' Theorem== | ||
− | The question can be translated into <math>P(\textnormal {Likes | + | The question can be translated into <math>P(\textnormal {Likes | Says Dislike})</math>. |
This is equal to the probability of <math>\frac{\textnormal{P(Likes} \cap \textnormal{Says Dislike)}}{\textnormal{P(Says Dislike)}}</math>. P(Likes <math>\cap</math> Says Dislike) = .6 <math>\cdot</math> .2 = .12. P(Says Dislike) = (.4 <math>\cdot</math> .9) + (.6 <math>\cdot</math> .2) = .48. .12/.48 = 25% | This is equal to the probability of <math>\frac{\textnormal{P(Likes} \cap \textnormal{Says Dislike)}}{\textnormal{P(Says Dislike)}}</math>. P(Likes <math>\cap</math> Says Dislike) = .6 <math>\cdot</math> .2 = .12. P(Says Dislike) = (.4 <math>\cdot</math> .9) + (.6 <math>\cdot</math> .2) = .48. .12/.48 = 25% |
Revision as of 11:59, 3 July 2024
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 .
This is equal to the probability of . P(Likes Says Dislike) = .6 .2 = .12. P(Says Dislike) = (.4 .9) + (.6 .2) = .48. .12/.48 = 25%
~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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