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# A certain junior class has 1000 students and a certain

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Intern
Joined: 06 Jan 2006
Posts: 23
Location: Illinois
A certain junior class has 1000 students and a certain [#permalink]

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19 Feb 2006, 13:58
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A certain junior class has 1000 students and a certain senior class has 800 students. Among these students there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the two students selected will be a sibling pair?

(A) 3/40000
(B) 1/3600
(C) 9/2000
(D) 1/60
(E) 1/15

This problem is fairly old and I have read the previous posts' explanations. But I'm still really confused about one thing.
So the probability of picking the first member of the sibling pair from the junior class is 60/1000. But how come the probability of picking the other member of the sibling pair from the senior class is 1/800?

I mean after you find the first guy from the junior class, you still need to find his brother/sister in the senior class, and you have to look for this person in that 60 pair siblings sample don't you?
I don't understand why the possibility becomes 1/800 for that second member of the sibling pair? Why are you saying this person could be 1 of 800 kids when he is very well 60 of 800 kids?

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Joined: 21 Sep 2003
Posts: 1057
Location: USA
Re: GMATPrep PS Probability Sibling Pair [#permalink]

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19 Feb 2006, 15:12
cattalk wrote:

I mean after you find the first guy from the junior class, you still need to find his brother/sister in the senior class, and you have to look for this person in that 60 pair siblings sample don't you?

cattalk,

P(finding sibling pair) = P(finding one of the 60 Jr among 1000)*P(finding his/her Senior sibling)

= (60/1000)*(1/800)

Alternatively, you could think in terms of number of combinations:
Total combinations = 1000*800

(J1,S1)(J2,S2)......(J60,S60).... 60 such pairs can be found.

P(finding sibling pair) = 60/(1000*800)
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Manager
Joined: 01 Feb 2006
Posts: 100
Re: GMATPrep PS Probability Sibling Pair [#permalink]

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19 Feb 2006, 16:05
cattalk wrote:
A certain junior class has 1000 students and a certain senior class has 800 students. Among these students there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the two students selected will be a sibling pair?

(A) 3/40000
(B) 1/3600
(C) 9/2000
(D) 1/60
(E) 1/15

This problem is fairly old and I have read the previous posts' explanations. But I'm still really confused about one thing.
So the probability of picking the first member of the sibling pair from the junior class is 60/1000. But how come the probability of picking the other member of the sibling pair from the senior class is 1/800?

I mean after you find the first guy from the junior class, you still need to find his brother/sister in the senior class, and you have to look for this person in that 60 pair siblings sample don't you?
I don't understand why the possibility becomes 1/800 for that second member of the sibling pair? Why are you saying this person could be 1 of 800 kids when he is very well 60 of 800 kids?

The probability of picking the first sibling is 60/1000 this is because it could be any one of the sixty. For our first choice we get to pick any one out of the 60 that has a sibling.
The probability of picking the second sibling is now 1/800. This is because this time we can't just pick a random sibling like the first time since. The second one has to actually be related to the first.

Another way to think about it for more clarity:
Do it the other way round. Let's say we pick the junior sibling first the probability will be 60/800. Now when we pick the second sibling (senior sibling), the probabiity is now 1/1000 since there is only on possible choice. This would give us (60/800)(1/1000), which factors out to the same as above.
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

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19 Feb 2006, 18:47
First pick from junior class, then we can pick any of the possible 60 pairs, thus P = 60/1000 = 3/50

But second pick from senior class must be the sibling of the one we picked from the junior class, and there is only 1 such sibling, so P = 1/800

We're not concerned about position, so we do not need to consider the first pick from the senior class and the second pick from the junior class (that is, no need to multiply the answer by 2)

P = 3/50 * 1/800 = 3/40,000
19 Feb 2006, 18:47
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