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# ps tricky one

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Senior Manager
Joined: 30 May 2005
Posts: 277
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ps tricky one [#permalink]  07 Sep 2005, 03:03
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Question Stats:

100% (02:24) correct 0% (00:00) wrong based on 0 sessions
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
Intern
Joined: 04 Sep 2005
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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.
Intern
Joined: 10 Jun 2004
Posts: 44
Location: Boston, MA
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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
VP
Joined: 13 Jun 2004
Posts: 1122
Location: London, UK
Schools: Tuck'08
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Kudos [?]: 31 [0], given: 0

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

Current Student
Joined: 28 Dec 2004
Posts: 3391
Location: New York City
Schools: Wharton'11 HBS'12
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Kudos [?]: 181 [0], given: 2

I get 1...

one of them will always be a pair...its a logical question not a probability one...
Senior Manager
Joined: 27 Aug 2005
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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.)
SVP
Joined: 03 Jan 2005
Posts: 2250
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Kudos [?]: 216 [0], given: 0

Sounds like this is a brain teaser isn't it?
_________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.

Intern
Joined: 27 Aug 2005
Posts: 33
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Can you please post the OA for this...

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

Sudha
Intern
Joined: 19 Aug 2005
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Kudos [?]: 1 [0], given: 0

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)

Senior Manager
Joined: 20 Dec 2004
Posts: 257
Followers: 6

Kudos [?]: 84 [0], given: 0

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 ?
Manager
Joined: 03 Aug 2005
Posts: 134
Followers: 1

Kudos [?]: 2 [0], given: 0

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.

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