please solve this one

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please solve this one

by sanjeevsinha01 » Tue Jul 20, 2010 4:32 am
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
c 5/7
e 16/21
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by kmittal82 » Tue Jul 20, 2010 4:45 am
Let the people be A B C D E F G

A is a sibling of B
C is a sibling of D
E F G are siblings of each other

So we have these siblings:
A-B
C-D
E-F-G

Number of ways of selecting 2 people from pair 1 (i.e. A-B) = 2C2 = 1

Number of ways of selecting 2 people from pair 2 (i.e. C-D) = 2C2 = 1

Number of ways of selecting 2 people from pair 3 (i.e. E-F-G) = 3C2 = 3

Total number of ways of selecting 2 people out of 7 = 7C2 = 21

Probability of selecting a sibling = 5/21
Thus, probability of not selecting a sibling pair = 1 - 5/21 = 16/21

Answer should be (E)
Last edited by kmittal82 on Tue Jul 20, 2010 4:45 am, edited 1 time in total.

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by Rahul@gurome » Tue Jul 20, 2010 4:45 am
If we select 2 persons from a group of 4 persons, then probability of selecting 2 person from group of 4 = 2C1 * 2C1 = 4

If we select 1 person from a group of 4 persons and 1 person from group of 3 persons, then probability of selecting 1 person from group of 4 and 1 from group of 3 = 4C1*3C1 = 12

Total probability = 7C2 = 21

Therefore, required probability = (4+12) /21 = 16/21

The correct answer is (E).
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by outreach » Tue Jul 20, 2010 4:59 am
there are 2 pairs of sibling and 3 sibling

2 people who are sibling can be selected from 2 pairs in 2 ways
2 people who are sibling from 3 sibling are=3c2=3


total possibility of selecting 2 people from 7 people is =7c2=21


probability that two individuals are siblings=(2+3)/21

two individuals are NOT siblings = 1 -5/21=16/21
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by GMATGuruNY » Tue Jul 20, 2010 8:32 am
P = (good outcomes)/(total possible outcomes)

total outcomes = total number of possible pairs that can be made from 7 choices = (7*6)/(1*2) = 21

A good outcome is if we don't choose a sibling pair. Let's count how many siblings pairs we have:

If ABC are all siblings (AB, AC, BC), that gives us 3 siblings pairs that account for the 3 people that have 2 siblings each.
This leaves 2 other sibling pairs, DE and FG, which account for the 4 people that have 1 sibling each.

So we have 3+2=5 sibling pairs.

This means we have 21-5=16 pairs that are NOT made of siblings.

So P(not a sibling pair) = 16/21.

The correct answer is E.
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