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by YellowSapphire » Thu Aug 05, 2010 4:55 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 and 1 law student. If 1 student is selected at random from both schools, what is the probability that a sibling pair is selected?
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by nithi_mystics » Thu Aug 05, 2010 5:10 am
3/40000

Prob of choosing one of the 30 from the business school = 30/500
Prob of choosing the sibling from the law school = 1/800

Prob of choosing the pair = 30/500 * 1/800
= 3/40000

What is the OA?
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by sanju09 » Thu Aug 05, 2010 5:21 am
YellowSapphire 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 and 1 law student. If 1 student is selected at random from both schools, what is the probability that a sibling pair is selected?

There are 30 students in the business school who have a sibling in the law school at the same university; hence there are 30 ways out of 500 for selecting one student from the business school who has a sibling in the law school. Once this is selected, we have a unique student in the law school consisting of 800 students, who is the sibling of this student selected from the business school, which could be done in just one way out of 800. The required probability is hence

= 30/500 × 1/800

= [spoiler]3/40000[/spoiler]

It won't alter the result if the first student is selected from the law school and the second from the business school.
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by frank1 » Thu Aug 05, 2010 6:23 am
ok to make it more clear

given,
Law=800
Business=500

sibling pair=30

asked:
If one pair is chosen whats probablity of getting sibling(find probability of getting sibling......or find probablity assuming that pair chosen was sibling...)

Either business student or law student can be chosen first
if Business school is chosen first
for 1st place 30 choices out of 500 30/500
for second time....no other choice actually...for it to be pair we must choose sibling of person who was chosen at first
so 1/800
so total
30/500 X 1/800

If we chose law student first it will be
30/800 X 1/500
which is same...

hope it helps someone...
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by YellowSapphire » Thu Aug 05, 2010 7:53 am
You are correct guy.
P = 3/40000
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by GMATGuruNY » Thu Aug 05, 2010 4:37 pm
YellowSapphire 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 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:

30 sibling pairs
500*800 = 400,000 total pairs
P(sibling pair) = 30/400,000 = 3/40,000
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by gig92 » Fri Aug 06, 2010 5:20 am
GMATGuruNY wrote:
YellowSapphire 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 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:

30 sibling pairs
500*800 = 400,000 total pairs
P(sibling pair) = 30/400,000 = 3/40,000


No offense but I would like to ask/clarify: Does 500*800 = 400,000 total pairs make sense in maths or is it just a trick?[/b]
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by GMATGuruNY » Fri Aug 06, 2010 5:33 am
gig92 wrote:
GMATGuruNY wrote:
YellowSapphire 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 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:

30 sibling pairs
500*800 = 400,000 total pairs
P(sibling pair) = 30/400,000 = 3/40,000


No offense but I would like to ask/clarify: Does 500*800 = 400,000 total pairs make sense in maths or is it just a trick?[/b]
No trickery; just sound mathematical reasoning.

From our source of business students, we have 500 choices.
From our source of law students, we have 800 choices.

To combine from multiple sources, we multiply the number of choices from each source.

Total possible combinations = 500*800 = 400,000.

If we had 300 business students and 400 law students, total ways to choose 1 from each school would be 300*400=120,000.
If we had 700 business students and 200 law students, total ways to choose 1 from each school would be 700*200=140,000.

Hope this helps!
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by garry123 » Tue Sep 14, 2010 2:14 pm
Why the following reasoning is wrong:

total number of students = 800+500 = 1300

total of number of sibling pairs = 30
= total number of students having the tag of sibling = 2*30 = 60

thus probability = 60/1300 = 6/130

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by Ian Stewart » Thu Sep 16, 2010 8:51 am
garry123 wrote:Why the following reasoning is wrong:

total number of students = 800+500 = 1300

total of number of sibling pairs = 30
= total number of students having the tag of sibling = 2*30 = 60

thus probability = 60/1300 = 6/130
The question in the original post is actually an almost word-for-word copy of a question in the Official Guide (with a few details changed). You can see the OG version here:

www.beatthegmat.com/a-sibling-pair-t34354.html

I'm curious where the question is from. I've been seeing a lot of these nearly exact replicas of OG problems posted in this forum, and if they're being sold by a company as 'original problems', that would seem like false advertising to me; a problem is not 'original' (or particularly helpful to test takers) if it's copied from the OG with a few numbers changed. In any case, whoever 'copied' this question did not do a good job of it, since he or she changed an important word:
YellowSapphire 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 and 1 law student. If 1 student is selected at random from both schools, what is the probability that a sibling pair is selected?
In the OG version, the word 'both' (highlighted above) actually reads 'each'. So the OG question makes clear that you are choosing two students, one from each class. In the imitation question above, the word 'both' is imprecise; one could easily interpret the phrase "if one student is selected... from both schools" to mean that we will select a single student from the group of all students attending either school.

That's the interpretation garry123 made in his post above, and it's a reasonable interpretation from the wording of the question. So garry has answered the question: if you pick one student from the 1300 students at either school, what is the probability that he or she belongs to a sibling pair? While the wording of the question does not make this clear, the intended question here is 'if you pick one student from the law school and one from the business school, what's the probability they are siblings?'
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