|
Author |
Message |
|
TAGS:
|
|
|
Intern
Joined: 31 May 2006
Posts: 45
Followers: 0
Kudos [?]:
0
[0], given: 0
|
In a room filled with 7 people, 4 people have exactly 1 [#permalink]
 17 Jul 2006, 17:47
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. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT friends?
5/21
3/7
4/7
5/7
16/21
Can someone please show me a quick way to approach this question. I figured it out but it's taken me way too long..
SQ
|
|
|
|
|
|
|
Senior Manager
Joined: 07 Jul 2005
Posts: 407
Location: Sunnyvale, CA
Followers: 2
Kudos [?]:
1
[0], given: 0
|
Total selections = 21
Consider A B C D E F G
There can be 5 set of friends
consider AB CD EF FG GE
prob of choosing friends = 5/21
not choosing friends = 16/21 (E)
|
|
|
|
|
|
Manager
Joined: 04 Jul 2006
Posts: 59
Followers: 1
Kudos [?]:
1
[0], given: 0
|
Let's call the seven people ABCD EFG (ABCD have only one friend, EFG have two friends).
Assumption: If X is a friend of Y, then Y is a friend of X ("a friendship") for any X,Y (element of ABCDEFG, x is not y).
If this assumption is correct, then it is pretty easy to calculate the probabilities:
Consider the first person, that is selected randomly.
In 4 of 7 cases, this person has only friend.
Hence the probability that the other person isn't his friend is 4/7*5/6=20/42.
In 3 of 7 cases, this person has two friends.
Hence the probability that the other person isn't his friend is 3/7*4/6=12/42.
Putting both cases together yields: 20/42+12/42=32/42=16/21.
Therefore E.
|
|
|
|
|
|
GMAT Instructor
Joined: 04 Jul 2006
Posts: 1278
Location: Madrid
Followers: 9
Kudos [?]:
69
[0], given: 0
|
Nicely done!
Or, think of three groups of people
Group 1: abc
Group 2: de
Group 3: fg
Number of ways of choosing 2 people 6C2=21
Number of ways of choosing 2 friends 3+1+1=5
Therefore, the probability that the two chosen people are not friends is (21-5)/21= 16/21
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Similar topics |
Author |
Replies |
Last post |
|
Similar
Topics:
|
 |
|
|
In a room filled with 7 people, 4 people have exactly 1
|
cool_jonny009 |
2 |
13 Feb 2006, 11:22 |
|
|
|
|
In a room filled with 7 people, 4 people have exactly 1
|
X & Y |
7 |
23 Jun 2006, 20:38 |
 |
|
|
In a room filled with 7 people, 4 people have exactly 1
|
LM |
12 |
22 May 2007, 00:24 |
|
|
|
 |
In a room filled with 7 people, 4 people have exactly 1
|
Skewed |
5 |
18 Nov 2007, 12:48 |
|
|
|
|
In a room filled with 7 people, 4 people have exactly 1
|
applecrisp |
1 |
09 Dec 2007, 15:09 |
|
|
|
|
|
|
close
