Probability of selecting siblings

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LulaBrazilia: Master | Next Rank: 500 Posts; Posts: 116; Joined: Tue Mar 31, 2009 10:50 amFollowed by: 1 member

by LulaBrazilia » Tue Mar 11, 2014 7:00 pm

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) 1/16

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Source: Beat The GMAT — Problem Solving | Tue Mar 11, 2014 7:00 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Mar 11, 2014 7:07 pm

LulaBrazilia wrote: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) 1/16

One option is to apply probability rules.

So, for two siblings to be selected, 2 things must happen: we must select a junior who has a senior sibling AND the senior selected must be the sibling of the selected junior.
We get P(junior with sibling AND selected senior is sibling to selected junior)= P(junior with sibling) x P(selected senior is sibling to selected junior)

P(junior with sibling): there are 1000 juniors and 60 of them have senior siblings. So, P(junior with sibling)=60/1000

P(selected senior is sibling to selected junior): Once the junior has been selected, there is only 1 senior (out of 800 seniors) who is the sibling to the selected junior. So, P(selected senior is sibling to selected junior)= 1/800

So, the probability is (60/1000)x(1/800) = 3/40,000
The answer is A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

by Patrick_GMATFix » Tue Mar 11, 2014 7:08 pm

There are 60/1,000 chances to pick a sibling from the junior class, then only 1/800 chances to pick the matching sibling from the senior class. The probability that both happen is (60/1000)(1/800) = 3/40,000. The answer is A. I go through the question in detail in the full solution below (taken from the GMATFix App).

-Patrick

Check out my site: GMATFix.com

To prep my students I use this tool >> (screenshots, video)

Ask me about tutoring.

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