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

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

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

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.

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