Probability

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

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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Source: Beat The GMAT — Problem Solving | Tue Oct 18, 2011 1:26 am

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Anurag@Gurome: GMAT Instructor; Posts: 3835; Joined: Fri Apr 02, 2010 10:00 pmFollowed by: 523 members; Location: Milpitas, CA; Thanked: 1854 times; GMAT Score:770

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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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

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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saketk: Legendary Member; Posts: 608; Joined: Sun Jun 19, 2011 11:16 amFollowed by: 8 members; Thanked: 37 times

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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