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In a group of 11 members, 5 have 4 siblings each and 6 have one

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In a group of 11 members, 5 have 4 siblings each and 6 have one [#permalink]

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In a group of 11 members, 5 have 4 siblings each and 6 have one sibling each. If two members are picked randomly, what is the probability that they are siblings?

A. \(\frac{16}{55}\)

B. \(\frac{13}{55}\)

C. \(\frac{10}{55}\)

D. \(\frac{6}{11}\)

E. \(\frac{17}{110}\)
[Reveal] Spoiler: OA

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In a group of 11 members, 5 have 4 siblings each and 6 have one [#permalink]

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nkmungila wrote:
In a group of 11 members, 5 have 4 siblings each and 6 have one sibling each. If two members are picked randomly, what is the probability that they are siblings?

A. \(\frac{16}{55}\)

B. \(\frac{13}{55}\)

C. \(\frac{10}{55}\)

D. \(\frac{6}{11}\)

E. \(\frac{17}{110}\)


5 have 4 siblings each implies that there is one group of 5 siblings {1 - 2 - 3 - 4 - 5} (notice that each of these 5 have 4 siblings);
6 have one sibling each implies that there are three groups of 2 siblings {6 - 7}, {8 - 9}, {10 - 11}.

The total number of ways to choose two people out of 11 is 11C2 = 11!/(2!9!) = 55.

In order to get two siblings we can choose any two from {1 - 2 - 3 - 4 - 5}, so 5C2 = 10 cases or any of the three sibling pairs: {6 - 7}, {8 - 9} or {10 - 11}, so 3 cases.

P = (10 + 3)/55 = 13/55.

Answer: B.
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Re: In a group of 11 members, 5 have 4 siblings each and 6 have one [#permalink]

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New post 30 Oct 2017, 23:34
Bunuel wrote:
nkmungila wrote:
In a group of 11 members, 5 have 4 siblings each and 6 have one sibling each. If two members are picked randomly, what is the probability that they are siblings?

A. \(\frac{16}{55}\)

B. \(\frac{13}{55}\)

C. \(\frac{10}{55}\)

D. \(\frac{6}{11}\)

E. \(\frac{17}{110}\)


5 have 4 siblings each implies that there is one group of 5 siblings {1 - 2 - 3 - 4 - 5};
6 have one sibling each implies that there are three groups of 2 siblings {6 - 7}, {8 - 9}, {10 - 11}.

The total number of ways to choose two people out of 11 is 11C2 = 11!/(2!9!) = 55.

In order to get two siblings we can choose any two from {1 - 2 - 3 - 4 - 5}, so 5C2 = 10 cases or any of the three sibling pairs: {6 - 7}, {8 - 9} or {10 - 11}, so 3 cases.

P = (10 + 3)/55 = 13/55.

Answer: B.


Similar question: https://gmatclub.com/forum/in-a-room-fi ... 87550.html
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In a group of 11 members, 5 have 4 siblings each and 6 have one [#permalink]

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New post 30 Oct 2017, 23:48
nkmungila wrote:
In a group of 11 members, 5 have 4 siblings each and 6 have one sibling each. If two members are picked randomly, what is the probability that they are siblings?

A. \(\frac{16}{55}\)

B. \(\frac{13}{55}\)

C. \(\frac{10}{55}\)

D. \(\frac{6}{11}\)

E. \(\frac{17}{110}\)



Hi....

5 have 4 siblings each means these 5 are siblings
6have 1 sibling each means there are 3 pair of siblings.

So two ways to solve..

1) finding prob of picking siblings..
As also explained above by bunuel...
Picking 2 out of 5 siblings =5C2=10
Picking 2 of the two siblings=2C2=1, three such pairs so 3 ways..
Total 10+3=13..
Ways to pick up 2 out of 11=11C2=11*10/2=55

Prob =13/55

2) prob of not picking siblings
Pick up 1 of these 5siblings and SECOND can be any of remaining 6, so 5*6=30
Pick up 1 of the two siblings and SECOND can be any of 11-2 or 9, so 2*9..
Three such pairs=2*9*3=54

Total 30+54=84..
Way to pick up 2 =11*10
So prob of not picking=84/11*10=84/110=42/55
So prob of picking=1-42/55=13/55

B
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Re: In a group of 11 members, 5 have 4 siblings each and 6 have one [#permalink]

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New post 01 Nov 2017, 17:11
nkmungila wrote:
In a group of 11 members, 5 have 4 siblings each and 6 have one sibling each. If two members are picked randomly, what is the probability that they are siblings?

A. \(\frac{16}{55}\)

B. \(\frac{13}{55}\)

C. \(\frac{10}{55}\)

D. \(\frac{6}{11}\)

E. \(\frac{17}{110}\)


Of the 5 people who have 4 siblings each, they must be each others’ siblings. Of the 6 people who have 1 sibling each, there must be 3 pairs of people who are siblings of each another.

When 2 people are picked randomly, the probability that they are 2 people from the 5-people siblings is:

5/11 x 4/10 = 20/110

The probability that they are 2 people from any of the 3 pairs of siblings is:

(2/11 x 1/10) x 3 = 6/110

Thus, the overall probability is 20/110 + 6/110 = 26/110 = 13/55.

Answer: B
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Re: In a group of 11 members, 5 have 4 siblings each and 6 have one   [#permalink] 01 Nov 2017, 17:11
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