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# A certain junior class has 1,000 students and a certain

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Intern
Joined: 26 Apr 2009
Posts: 6
A certain junior class has 1,000 students and a certain [#permalink]

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20 May 2009, 00:15
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A certain junior class has 1,000 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 2 students selected will be a sibling pair?

A) 3 / 40,000
B) 1 / 3,600
C) 9 / 2,000
D) 1 / 60
E) 1 / 15
Intern
Joined: 06 Apr 2009
Posts: 2
Re: probability problem from OG [#permalink]

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20 May 2009, 00:27
60/1000 * 60/800 = 9/2000

Ans is C
Intern
Joined: 26 Apr 2009
Posts: 6
Re: probability problem from OG [#permalink]

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20 May 2009, 00:33
pursue800 wrote:
60/1000 * 60/800 = 9/2000

Ans is C

imho that is the probability that each of the 2 students has a sibling in the other class. That does not mean that they form a pair.
Manager
Joined: 21 May 2009
Posts: 120
Re: probability problem from OG [#permalink]

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21 May 2009, 12:57
aismirnov wrote:
pursue800 wrote:
60/1000 * 60/800 = 9/2000

Ans is C

imho that is the probability that each of the 2 students has a sibling in the other class. That does not mean that they form a pair.

selection of first student 60/1000 and selection of second student is 1/800
so ans is :- 3/40000 A?
Intern
Joined: 02 Mar 2009
Posts: 43
Location: Austin
Re: probability problem from OG [#permalink]

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21 May 2009, 19:45
Agreed.

One question: Can you reason as to why we shouldn't also consider (60/800) * (1/1000). In other words why don't' we do the following:

(60/800) * (1/1000) + (60/1000) * (1/800)
Intern
Joined: 26 Apr 2009
Posts: 6
Re: probability problem from OG [#permalink]

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21 May 2009, 22:12
Actually, it seems that you are 2 times right
The probability we need is
60/(800*1000)

The explanation is as follows:
the probability a junior student with a sibling in the other class is selected at random is 60/1000. Given this the probability the match is randomly chosen in the senior class is 1/800.
Multiply the probabilities (independent events) and you will arrive at 60/(800*1000)

Otherwise, we could say that the number of all possible pair of students (one from junior class and one from senior class) is 800*1000. The number of relevant pairs is 60. Picking one junior student and one senior student at random is equivalent to picking a pair of students at random. Thus, the probbility of picking a relevant pair is 60/(800*1000)
Re: probability problem from OG   [#permalink] 21 May 2009, 22:12
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