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Probability

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by shankar.ashwin » Tue Oct 18, 2011 1:26 am
The probability that the exam is held at centre A,B or C is equally likely. The probability Tom passes the exam when writing it at the respective centres is 2/3 , 2/3 , and 1/3. What is the probability that Tom wrote the exam at centre A if he passed the exam?

A) 1/3
B) 2/3
C) 2/5
D) 2/15
E) 1/8
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by Anurag@Gurome » Tue Oct 18, 2011 1:53 am
shankar.ashwin wrote:The probability that the exam is held at centre A,B or C is equally likely. The probability Tom passes the exam when writing it at the respective centres is 2/3 , 2/3 , and 1/3. What is the probability that Tom wrote the exam at centre A if he passed the exam?
This is a question of joint conditional probability, which I don't think is a part of GMAT syllabus.

Anyway, here is the solution...
Say, the probability that Tom passed the exam = P(P)
Say, the probability that Tom wrote the exam at center A and passed = P(AP)
Say, the probability that Tom wrote the exam at center A if he passed = P(A|P)

P(P) = (1/3)*(2/3) + (1/3)*(2/3) + (1/3)*(1/3) = 5/9
P(AP) = (1/3)*(2/3) = 2/9

Now, P(A|P) = P(AP)/P(P) = (2/9)/(5/9) = 2/5

The correct answer is C.
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by shankar.ashwin » Tue Oct 18, 2011 2:10 am
Pls ignore if it isn't in the scope of that GMAT. I thought it was a variant of a normal probability question.
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by saketk » Tue Oct 18, 2011 9:47 am
shankar.ashwin wrote:Pls ignore if it isn't in the scope of that GMAT. I thought it was a variant of a normal probability question.
where did you pick this from? CAT question?
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