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PS probability 700-800

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Intern
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PS probability 700-800 [#permalink] New post 04 Jul 2010, 23:39
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A
B
C
D
E

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Question Stats:

75% (02:17) correct 25% (00:00) wrong based on 4 sessions
I don't quite understand how to solve this problem... Especially the paring sibling part. Please explain, much appreciated!

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?

5/21
3/7
4/7
5/7
16/21

Thank YOU
[Reveal] Spoiler: OA
Intern
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Re: PS probability 700-800 [#permalink] New post 04 Jul 2010, 23:40
ahh Oops, wrong section.....sorry...
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Re: PS probability 700-800 [#permalink] New post 05 Jul 2010, 13:52
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Four people have exactly one sibling and three people have exactly two siblings.

Think about how this can be done...the only way to organize is this is to have two pairs of siblings and one trio of siblings. In other words:

AB (one sibling pair)
CD (another sibling pair)
EFG (a trio of siblings)

This way each of A and B are siblings, each of C and D are siblings, so we have four people each with exactly one sibling. And each of E, F, and G are siblings so we have three people each of whom has exactly two siblings.

Because this is a "NOT" probability question, we should see how many ways we CAN select two individuals who are siblings.

Well, we can select the AB pair or the CD pair. So far, that's 2 ways. We can also select any two people from the EFG trio, so that's another 3C2 or 3 ways.

So, there are a total of 2+3 = 5 ways of pulling out 2 individuals who are siblings.

Probability = (#desired)/(#total)

The denominator of the formula is just all the ways we can select any two people from the seven. So we have:

Probability of selecting 2 people who are siblings = 5/7C2 = 5/21

Therefore, the probability of selecting 2 people who are NOT siblings is:

1 - 5/21 = 16/21

Choose E.
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Re: PS probability 700-800 [#permalink] New post 05 Jul 2010, 16:42
That is one way, I think it is easier to calculate the probabilities than the combinations.

there is 4/7 chance of selecting a person with one sibling initially with a 5/6 probability the second person will not be a sibling.

There is a 3/7 Chance of selecting a person with 2 siblings initially with 4/6 probability the second person will not be a sibling.

Simply adding these probabilities together gives you the answer.

4/7 * 5/6 + 3/7 * 4/6 = 20/42 + 12/42 = 32/42 = 16/21
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Re: PS probability 700-800 [#permalink] New post 05 Jul 2010, 17:39
Great explanations guys.

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+1 kudos me if this is of any help...

Re: PS probability 700-800   [#permalink] 05 Jul 2010, 17:39
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