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ps tricky one

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07 Sep 2005, 03:03
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HEllo
plz need help on this one plz explain your works and reasoning
thanks

Badri has 9 pairs of dark Blue socks and 9 pairs of Black socks. He keeps them all in a same bag. If he picks out three socks at random what is the probability he will get a matching pair?

(1) (2*9C2 * 9C1) / 18C3 (2) (9C2 * 9C1) / 18C3
(3) 1 (4) None of these
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07 Sep 2005, 03:13
mandy wrote:
(1) (2*9C2 * 9C1) / 18C3
(2) (9C2 * 9C1) / 18C3
(3) 1
(4) None of these

I may misunderstand this question but no matter what he will get at least 2 socks of the same color so no matter what he will have a pair of the same color.
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07 Sep 2005, 08:12
I am not sure, but may be this is the solution.
Total outcomes equal 18C3

Chosing 2 same color socks out of 3 equals 3C2

P=3C2/18C3 = 3/816
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07 Sep 2005, 08:53
I consider each pair as a specific pair. so total would be 18 differents socks : so to get 1 pair out of 3 socks : 1/17+1/17*1/16=1/16

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07 Sep 2005, 09:29
I get 1...

one of them will always be a pair...its a logical question not a probability one...
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07 Sep 2005, 13:14
Ah, but anyone who knows fashion knows that not all black socks are created equal. There are the black knee socks, the short little black ankle socks, the ribbed black socks, the "nearly grey from being washed so often" black socks, the "holes in the toes" black socks...

In my opinion, the question should specify that all black socks are homogeneous and all blue socks are homogeneous.

Then again, when was the last time personal opinion mattered on the GMAT?

(Long story short: assuming all black socks are identical and all blue socks are identical, probability is 1.)
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07 Sep 2005, 17:07
Sounds like this is a brain teaser isn't it?
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26 Sep 2005, 19:21
Can you please post the OA for this...

I think the probability is 1, but if anyone knows the solution, let me know.

Sudha
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26 Sep 2005, 22:10
whew.... pretty interesting.

i am getting

1/18*1/17*1/18+1/18*1/18*1/17+1/18*1/18*1/17= 3/(18*18*17)

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28 Sep 2005, 20:05
I would say (9C2 * 9C1) / 18C3

Total number of ways of selecting 3 socks = 18C3

Total number of ways of selecting 1 pair
= (1Black & 1 Bluer pair) or (1 Blue & 1 Black pair)
= (18*9C1) + (18*9C1)
= 2*(18*9C1) = (9C2*9C1)

Probability = (9C2 * 9C1) / 18C3

What is the OA ?
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28 Sep 2005, 23:20
I assume all socks of the same color are equal, answ: 1

Anyway, I was wondering why everyone keeps talking about 18 socks, as I understand it there are 9 pairs of each color, 18 of each color = 36.

28 Sep 2005, 23:20
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