Selection Problem

[akshatgupta87]

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..

[Stuart@KaplanGMAT]

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!

[sh.nada]

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

[Brent@GMATPrepNow]

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