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Probability

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by heshamelaziry » Mon Nov 16, 2009 9:58 pm
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?

OA [spoiler]16/21[/spoiler]
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by Abdulla » Mon Nov 16, 2009 11:12 pm
heshamelaziry wrote: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?

OA [spoiler]16/21[/spoiler]
I am bad with Probabilities but I will try it..

Prob = # desire outcomes / Total outcomes

Let's start with the easy one. We want to choose 2 out of 7.

Total outcomes = 7! / 2!5! = 21 ( 7 x 6 x 5 x 4 x 3 x 2 x 1 / 5 x 4 x 3 x 2 x 1 x 2 x 1 )

# of Desired outcomes. We've got two scenarios.
1) Choosing two people from the first group.
4! / 2!2! = 6 ..... ( remember that we've selected 2 people each of which has one sibling in the room, so we should subtract 2)
6-2 = 4 .......(1)

2) Choosing one from the first group times another from the second group.
4! /1!3! * 3! /2!1! = 4*3 = 12 ...........(2)

4+12 / 21 = 16/21 #
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by heshamelaziry » Mon Nov 16, 2009 11:34 pm
HOhw you say you are bad with probability ? you got the right answer. However, I am still lost.
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by Abdulla » Mon Nov 16, 2009 11:49 pm
heshamelaziry wrote:HOhw you say you are bad with probability ? you got the right answer. However, I am still lost.
I spent 15 minutes to figure it out. :D
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by heshamelaziry » Mon Nov 16, 2009 11:55 pm
Abdulla wrote:
heshamelaziry wrote:HOhw you say you are bad with probability ? you got the right answer. However, I am still lost.
I spent 15 minutes to figure it out. :D

Still very well done. I still can't rationalize it :x . BTW, did u get my pm ?
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by getso » Tue Nov 17, 2009 4:19 am
Hi ,

Could you please explain the logic...
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by viju9162 » Tue Nov 17, 2009 4:32 am
Hi Abdulla, heshamelaziry,

I didnt understand how you arrived at the answer. Can you explain how can we solve with this formula:

P (A) = 1 - P`(A).

Regards,
Viju
"Native of" is used for a individual while "Native to" is used for a large group
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by mridul_dave » Tue Nov 17, 2009 6:35 am
heshamelaziry wrote: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?

OA [spoiler]16/21[/spoiler]
Lets say letters represents a person and a '--' represents the sibling relation.

A -- B
B -- C
these are the 4 people who have exactly one sibling.


E -- F
\ /
G

There are the three people with exactly two siblings each. We have total 7 people.

We just made three sets of people.

Lets get the prob. that two are siblings. For that either you pick from the first set, or second set or any two from the third set.

2C2 + 2 C2 + 3C2 = 1 + 1 + 3 = 5

Total ways is 7C2 = 21. Prob that two are siblings is 5/21.
So prob they are not is 1 - 5/21 = 16/21.
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by getso » Tue Nov 17, 2009 6:51 am
Thanks for the great explaination ..

:)
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by Abdulla » Tue Nov 17, 2009 11:29 pm
mridul_dave wrote:
heshamelaziry wrote: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?

OA [spoiler]16/21[/spoiler]
Lets say letters represents a person and a '--' represents the sibling relation.

A -- B
B -- C
these are the 4 people who have exactly one sibling.


E -- F
\ /
G

There are the three people with exactly two siblings each. We have total 7 people.

We just made three sets of people.

Lets get the prob. that two are siblings. For that either you pick from the first set, or second set or any two from the third set.

2C2 + 2 C2 + 3C2 = 1 + 1 + 3 = 5

Total ways is 7C2 = 21. Prob that two are siblings is 5/21.
So prob they are not is 1 - 5/21 = 16/21.
WOW, Easy approach..
Thanks hesham
Abdulla
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