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# In a room filled with 7 people, 4 people have exactly 1 sibling in the room and 3 people have exactly 2 siblings

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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

### 1 Best Answer

1

divide 7 people into 2 groups: Group 1 including 4 people have exactly 1 sibling and Group 2 including 3 people have exactly 2 siblings
First person:
If he is from G1 (probability: 4/7), the probability that the second one is not his sibling: 5/6 so 4/7*5/6=10/21
If he is from G2 (probability: 3/7), the probability that the second one is not his sibling: 4/6 so 3/7*4/6=6/21
10/21+6/21=16/21

answered Jul 2, 2014 by Senior Associate (475 points)
selected Sep 10, 2014
how does one arrive at 5/6 and 4/6?
commented Jan 7, 2015 by Beginner (1 point)
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