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Probability of siblings in school

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by rohit_gmat » Mon Oct 17, 2011 4:40 am
A certain business school has 500 students, and the law school at the same university has 800 students. Among these students, there are 30 sibling pairs consisting of 1 business student & 1 law student. If 1 student is selected at random from both schools, what is the probability that a sibling pair is selected?

A) 3/ 40,000
B) 3/ 20,000
C) 3/ 4,000
D) 9/ 400
E) 6/ 130

OA A

My question is to do with the wordings in this question... do they mean that they picked one student (from the both the schools put together) and they are asking what the probability is for that one student to have a sibling? Or do they mean that they pick one student from each school and want to know what the probability is that the 2 students happen to be siblings? Anyone else also facing the same prob?

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by shankar.ashwin » Mon Oct 17, 2011 4:47 am
I guess it should be 1 student eachwas picked up from both classes. But they do mention sibling pair, so you can understand they pick 2

First pick up anyone who has a sibling from the Business school - 30/500.

He has exactly one sibling in the other class of 800 - 1/800

So Prob = 3/50 * 1/800 = 3/40000 A
Last edited by shankar.ashwin on Mon Oct 17, 2011 4:53 am, edited 1 time in total.
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by gmatclubmember » Mon Oct 17, 2011 4:49 am
rohit_gmat wrote:A certain business school has 500 students, and the law school at the same university has 800 students. Among these students, there are 30 sibling pairs consisting of 1 business student & 1 law student. If 1 student is selected at random from both schools, what is the probability that a sibling pair is selected?

A) 3/ 40,000
B) 3/ 20,000
C) 3/ 4,000
D) 9/ 400
E) 6/ 130

OA A

My question is to do with the wordings in this question... do they mean that they picked one student (from the both the schools put together) and they are asking what the probability is for that one student to have a sibling? Or do they mean that they pick one student from each school and want to know what the probability is that the 2 students happen to be siblings? Anyone else also facing the same prob?
Thanks
Your second statement is what the question asks.
The probability will be
selecting one of the siblings from the 30 students out of 500 (30/500) and then selecting the one student from law school who is the sibling of the selected student (1/800)
Probability = 30/(500*800)=3/40000
Answer A[/u]
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by tpr-becky » Mon Oct 17, 2011 4:20 pm
You are correct, the more clear english would have said one student is selected from each school. however, they are asking you to select one from each and find the probability that the result is a sibling pair.

Therefore:

From the first school there are 30 people who are part of a sibling pair and we must pick one of these therefore the first probability is 30/500.

At the next school we need the exact sibling in order to have a sibling pair - thus the probabiliyt is 1/ 800

you multiply the two probabilities to get 30/(500x800) = 3/40000 - which is A.
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