At certain college, the senior class

Question

Source:Time
explain how to solve this

I agree with the first part that selecting a senior is 80/900 but after that i feel that while selecting a junior it shud be 80/1100. I am nt able to understand why this is wrong

At certain college, the senior class has 900 students and the junior class has 1100 students.
Among these 2000 students there are 80 sibling pairs, each consisting of one senior and one junior. A student is to be selected from each class.
In the table below, identify the number that represents the probability that the two students selected would form a sibling pair (P1). Also identify the number that represents the probability that the two Students selected are not siblings (P2).

GMATGuruNY · Answer

The problem above is modeled after the following problem in GMATPrep:

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 2 students selected will be sibling pair
1) 3/40,000
2)1/3,600
3)9/2,000
4)1/60
5)1/15

P(sibling pair) = (total number of sibling pairs)/(total number of possible pairs).

Total number of possible pairs:
There are 1000 juniors and 800 seniors.
Total number of ways to combine 1 junior with 1 senior = 1000*800 = 800,000.

Total number of sibling pairs = 60.

Thus:
P(sibling pair) = 60/800,000 = 3/40,000.

The correct answer is A.

Alternate approach:

Junior class:
P(picking a member of a sibling pair) = 60/1000. (Of the 1000 juniors, 60 belong to a sibling pair.)

Senior class:
P(picking the selected junior's sibling) = 1/800. (Of the 800 seniors, 1 is the selected junior's sibling).

Since we want both events to happen, we MULTIPLY the probabilities:
(60/1000) * (1/800) = 60/800000 = 3/40000.

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conquistador · Answer

Hello Mitch hunt,

Junior class:
P(picking a member of a sibling pair) = 60/1000. (Of the 1000 juniors, 60 belong to a sibling pair.) I completely agree with this.

but in

Senior class:
P(picking the selected junior's sibling) = 1/800. (Of the 800 seniors, 1 is the selected junior's sibling).
Why cant this be 60/800(Of the 800 juniors, 60 belong to a sibling pair.)

GMATGuruNY · Answer

Mechmeera wrote:Hello Mitch hunt,

Junior class:
P(picking a member of a sibling pair) = 60/1000. (Of the 1000 juniors, 60 belong to a sibling pair.) I completely agree with this.

but in

Senior class:
P(picking the selected junior's sibling) = 1/800. (Of the 800 seniors, 1 is the selected junior's sibling).
Why cant this be 60/800(Of the 800 juniors, 60 belong to a sibling pair.)

Let's say that junior A and senior B are siblings and that junior A has been selected from the junior class.
Once A has been selected, we cannot select from the senior class any of the 60 students belonging to a sibling pair.
Rather, we must select SENIOR B.
Thus, ONLY 1 OUTCOME from the senior class is favorable: SENIOR B.

Implication:
Once a junior has been selected, only 1 of the 800 seniors is a favorable outcome:
THE SIBLING OF THE JUNIOR ALREADY SELECTED.

Brent@GMATPrepNow · Answer

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 each school, what is the probability that a sibling pair is selected?

A) 3/40000
B) 3/20000
C) 3/4000
D) 9/400
E) 6/130

OAA

Here's another approach:

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
= [spoiler]3/40,000[/spoiler]
= 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

Brent Hanneson - Creator of GMATPrepNow.com

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