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Puzzling probability question

This topic has 3 expert replies and 4 member replies

Puzzling probability question

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Attached is the probability question.

Shouldn't answer to this question be B?

There are two possibilities as I can see:
30/500 * 1/800 + 30/800 * 1/500

Thanks,
Swapnil
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Master | Next Rank: 500 Posts
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This is an AND probability problem. Formula A*B
So you need to multiply two numbers to get your answer.

First Number (Probability of selecting a business student who has a sibling in the law school):
There are 500 business students, of which 30 have siblings in the law school. Probability of randomly selecting a business student who has a sibling at the law school is 30/500

There are 800 students in the law school, but only one can be a sibling of the business student we randomly selected. Probability of random selection is 1/800

Probability that we randomly select a sibling pair from the business school and law school:

30/500*1/800 = 3/40,000

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Junior | Next Rank: 30 Posts Default Avatar
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Shouldn't this should be AND & OR problem.

(Probability of selecting a business student who has a sibling in the law school) OR (Probability of selecting a law student who has a sibling in the business school) =
30/500 * 1/800 + 30/800 * 1/500

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spucmu wrote:
Shouldn't this should be AND & OR problem.

(Probability of selecting a business student who has a sibling in the law school) OR (Probability of selecting a law student who has a sibling in the business school) =
30/500 * 1/800 + 30/800 * 1/500
Not an And/Or problem. Just And. If you wanted to select the law student first and then the business school student, the formula would be 30/800*1/500 which still yields the same answer 3/40000

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GMAT/MBA Expert

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Quote:
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 and 1 law student. If 1 student is selected at random from both schools, what is the probability that a sibling pair is selected?
It might be easier to look at the problem this way:

A pair is to be formed by choosing 1 student from the business school and 1 student from the law school.
Number of choices from the business school = 500.
Number of choices from the law school = 800.
Total number of ways to choose a pair = 500*800 = 400,000.

Of these 400,000 pairs, the number of sibling pairs = 30.

P(sibling pair) = 30/400,000 = 3/40,000.

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Newbie | Next Rank: 10 Posts Default Avatar
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Hi GMATGuruNY,

I also faced this problem while giving a test, and i did the same mistake as mentioned in post above, I treated the question in similar fashion : -
(Probability of selecting a business student who has a sibling in the law school) OR (Probability of selecting a law student who has a sibling in the business school)
But obviously i was wrong.
How to decide when using to use OR and when to use AND. I certainly could not figure this out on this question.

Thanks
Dinesh

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GMAT/MBA Expert

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spucmu wrote:
Attached is the probability question.
P(selecting a sibling pair) = P(select a business student with a sibling AND select a law student who is that business student's sibling)
= P(select a business student with a sibling) x P(select a law student who is that business student's sibling)
= 30/500 x 1/800
= 30/400,000
= 3/40,000
= A

Note: P(select a business student with a sibling) = 30/500, because 30 of the 500 business students have a sibling in law school.
P(select a law student who is that business student's sibling) = 1/800, because there are 800 law students and only 1 is the sibling of the selected business student.

Cheers,
Brent

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spucmu wrote:
Attached is the probability question.

The probability of selecting from the business school any one sibling from the 30 sibling pairs is 30/500. Once that person is selected, the probability of selecting his or her sibling from the law school is 1/800; thus, the probability of selecting a sibling pair is:

30/500 x 1/800 = 3/50 x 1/800 = 3/40000

Alternatively, the probability of selecting from the law school any one sibling from the 30 sibling pairs is 30/800. Once that person is selected, the probability of selecting his or her sibling from the business school is 1/500; thus, the probability of selecting a sibling pair is:

30/800 x 1/500 = 3/80 x 1/500 = 3/40000

Answer: A

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