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Short-cut for Probability Ques

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Short-cut for Probability Ques

by MegW » Mon Nov 26, 2012 8:46 am
Ques 1:
Of 7 people, 4 have exactly 1 friend and 3 have exactly 2. If 2 people selected at random, what is the probability that they are not friends?

Soln 1:Shortcut:

Image

no. of friendships = 5

total no. = 7C5 = 21

P (friends) = 5/21

So P (not friends) = 16/21 {Answer is correct}

Ques 2.
Of 9 people, 6 have exactly 1 friend and 3 have exactly 2. If 2 people selected at random, what is the probability that they are not friends?

Soln 2:Shortcut:

Image

no. of friendships = 6

total no. = 9C6 = 84

P (friends) = 6/84= 1/14

So P (not friends) = 13/14 {incorrect}

Actually the no. of friendships should come equal to 7, so that 9C7= 36 & P(f) = 1/6 & P(nf)=5/6 {correct}

What mistake am I making in ques 2? or is the short cut method only not universal? Pls help. Thnks
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by Anindya Madhudor » Mon Nov 26, 2012 2:56 pm
You are making mistake in determining how many ways two people can be selected simultaneously from a group of people.

In the first example, the number of ways two people can be selected simultaneously from 7 people is 7C2 (which happens to be same as 7C5).

In the second case, it should be 9C2.
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by MegW » Mon Nov 26, 2012 10:40 pm
Hi Anindya! Thank you. Ya it was pretty simple but i was getting confused. Thanks for clearing it up!
Anindya Madhudor wrote:You are making mistake in determining how many ways two people can be selected simultaneously from a group of people.

In the first example, the number of ways two people can be selected simultaneously from 7 people is 7C2 (which happens to be same as 7C5).

In the second case, it should be 9C2.
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