Selection Problem

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akshatgupta87: Senior | Next Rank: 100 Posts; Posts: 97; Joined: Wed Sep 01, 2010 11:11 amFollowed by: 2 members; Thanked: 1 times

by akshatgupta87 » Fri Apr 22, 2011 12:37 pm

Q.) In a room filled with 7 people, 4 people have exactly 1 sibling in the room and 3 people have exactly 2 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
A) 5/21
B) 3/7
C) 4/7
D) 5/7
E) 16/21
Someone explain..

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Source: Beat The GMAT — Problem Solving | Fri Apr 22, 2011 12:37 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

by Stuart@KaplanGMAT » Fri Apr 22, 2011 12:42 pm

Hi!

This question has been discussed many times - I ran a search on "4 people have exactly 1 sibling" and hit a ton of threads.

Here's one in which I explain the question:

https://www.beatthegmat.com/sibling-prob ... 46183.html

and there are many others if you don't click with that one!

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course

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sh.nada: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Mon Apr 18, 2011 2:52 am

by sh.nada » Sun Apr 24, 2011 5:04 am

Thanks Stuart

However, i have tried another approach to solve this question but i failed miserably.

i multiplied the probability of selecting the first NOT sibling by the Probability of selecting the second not sibling as follows

4/7 * 3/6 = 2/7 (not one of the answer choices)

kindly help me to understand how to approach such questions

Thank you

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GMAT/MBA Expert

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 » Sun Apr 24, 2011 5:33 am

sh.nada wrote:Thanks Stuart

However, i have tried another approach to solve this question but i failed miserably.

i multiplied the probability of selecting the first NOT sibling by the Probability of selecting the second not sibling as follows

4/7 * 3/6 = 2/7 (not one of the answer choices)

kindly help me to understand how to approach such questions

Thank you

The big problem with your approach is that everyone in the room is a sibling (there are 2 pairs of siblings and one trio of siblings).
So, the first person you select must be someone's sibling.
In your solution you begin by finding the probability of selecting the first NOT sibling, which you say is 4/7, but this probability must be zero, since it's impossible to select someone who is not a sibling.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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