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# In a room filled with 7 people, 4 people have exactly 1

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In a room filled with 7 people, 4 people have exactly 1 [#permalink]  15 Jan 2008, 11:03
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In a room filled with 7 people, 4 people have exactly 1 friend in the room and 3 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if John is Peter's friend, Peter is John's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?
A. 5/21
B.3/7
C. 4/7
D.5/7
E.16/21
CEO
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
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Kudos [?]: 2244 [1] , given: 359

Re: PS Room probability [#permalink]  15 Jan 2008, 11:52
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Expert's post
E

$$p=1-(\frac{4}{7}*\frac{1}{6}+\frac{3}{7}*\frac{2}{6})=\frac{16}{21}$$
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Last edited by walker on 16 Jan 2008, 09:54, edited 1 time in total.
CEO
Joined: 17 Nov 2007
Posts: 3574
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Followers: 414

Kudos [?]: 2244 [3] , given: 359

Re: PS Room probability [#permalink]  15 Jan 2008, 13:08
3
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Expert's post
bmwhype2 wrote:
what's 1/6?

p=1-(4/7*1/6+3/7*2/6)=16/21

4/7 - the probability to choose one of 4 people who have 1 friend.
1/6 - the probability to choose a friend of 6 remained people

3/7 - the probability to choose one of 3 people who have 2 friend.
2/6 - the probability to choose a friend of 6 remained people.
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Intern
Joined: 15 Jan 2008
Posts: 10
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Kudos [?]: 2 [1] , given: 0

Re: PS Room probability [#permalink]  16 Jan 2008, 08:28
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This is a tough question. What is the likelihood something like this will appear on the real GMAT?

JCLEONES wrote:
In a room filled with 7 people, 4 people have exactly 1 friend in the room and 3 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if John is Peter's friend, Peter is John's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?
A. 5/21
B.3/7
C. 4/7
D.5/7
E.16/21
Intern
Joined: 15 Jan 2008
Posts: 3
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Kudos [?]: 0 [0], given: 0

Re: PS Room probability [#permalink]  16 Jan 2008, 11:20
My answer is 16/21, but it took me a long time to do it.

JCLEONES wrote:
In a room filled with 7 people, 4 people have exactly 1 friend in the room and 3 people have exactly 2 friends in the room (Assuming that friendship is a mutual relationship, i.e. if John is Peter's friend, Peter is John's friend). If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?
A. 5/21
B.3/7
C. 4/7
D.5/7
E.16/21
CEO
Joined: 21 Jan 2007
Posts: 2760
Location: New York City
Followers: 9

Kudos [?]: 387 [0], given: 4

Re: PS Room probability [#permalink]  11 Feb 2008, 12:45
walker wrote:
bmwhype2 wrote:
what's 1/6?

p=1-(4/7*1/6+3/7*2/6)=16/21

4/7 - the probability to choose one of 4 people who have 1 friend.
1/6 - the probability to choose a friend of 6 remained people

3/7 - the probability to choose one of 3 people who have 2 friend.
2/6 - the probability to choose a friend of 6 remained people.

thanks. this question matches the senior / junior pair question in OG11.
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Re: PS Room probability   [#permalink] 11 Feb 2008, 12:45
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