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Siblings

by Jinglander » Tue Aug 10, 2010 7:50 pm
In a room filled with 7 people, 4 have 1 sibling and 3 have two siblings. If two people at selected at random what is the prob that they are not siblings.

Answer is 6/21

Can someone explain.
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by Rahul@gurome » Tue Aug 10, 2010 8:49 pm
Jinglander wrote:In a room filled with 7 people, 4 have 1 sibling and 3 have two siblings. If two people at selected at random what is the prob that they are not siblings.

Answer is 6/21

Can someone explain.
4 people have 1 sibling means there are 2 pairs of siblings.
Let A and B be the siblings, and C and D be the other pair of siblings.

Since 3 people have 2 siblings, so let E, F and G be the pair of 3 siblings.

Total no. of favorable ways of selecting 2 people from 7 people = 7C2 = 7!/(2!)(5!) = 21 ways
No. of favorable ways of selecting a sibling pair = 1 + 1 + 3 = 5 ways (We can select pairs from A-B, C-D, E-F, F-G, E-G)

Probability that they are siblings = 5/21
Probability that they not siblings = 1 - 5/21 = 16/21
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by sheelanadh » Wed Aug 11, 2010 4:24 am
Rahul@gurome wrote:
Jinglander wrote:In a room filled with 7 people, 4 have 1 sibling and 3 have two siblings. If two people at selected at random what is the prob that they are not siblings.

Answer is 6/21

Can someone explain.
4 people have 1 sibling means there are 2 pairs of siblings.
Let A and B be the siblings, and C and D be the other pair of siblings.

Since 3 people have 2 siblings, so let E, F and G be the pair of 3 siblings.

Total no. of favorable ways of selecting 2 people from 7 people = 7C2 = 7!/(2!)(5!) = 21 ways
No. of favorable ways of selecting a sibling pair = 1 + 1 + 3 = 5 ways (We can select pairs from A-B, C-D, E-F, F-G, E-G)

Probability that they are siblings = 5/21
Probability that they not siblings = 1 - 5/21 = 16/21
thank you....is the way of approach is correct..what is correct OA?
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