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Martin has a drawer containing 14 red socks,18 blue scoks

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Martin has a drawer containing 14 red socks,18 blue scoks [#permalink] New post 30 Jul 2003, 20:04
Martin has a drawer containing 14 red socks,18 blue scoks and some green socks,all mixed up together.If Martin pulls out one socks,the probability that it will be green is 1/3.

1)How many green socks are in the drawer.
2)If he takes out 3 socks,what is the probaility that he will get a matching pair.
3)If he takes out 2 socks ,what is the probability that he will get a matching pair.

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 [#permalink] New post 30 Jul 2003, 21:22
Martin has a drawer containing 14 red socks,18 blue scoks and some green socks,all mixed up together.If Martin pulls out one socks,the probability that it will be green is 1/3.

1)How many green socks are in the drawer.
2)If he takes out 3 socks,what is the probaility that he will get a matching pair.
3)If he takes out 2 socks ,what is the probability that he will get a matching pair.

1) let # of green socks be x
p(green sock pulled) = x/(14+18+x) = 1/3
Solving, x= 16

2) p(will get a matching pair out of 3 socks)
= 1 - p(three socks are unique)
= 1 - ((14*16*18)/(48*47*46))
= 1039/1081

3) P (will get a matching pair out of 2 socks)
= p(both red) + p(both blue) + p(both green)
= (14/48)*(13/47) + (18/48)*(17/47) + (16/48)*(15/47)
= 91/262

Akamai, please comment. Thanx
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P K Das

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 [#permalink] New post 31 Jul 2003, 04:34
I think the solution for the 2 task is the following:

p=1-1C14*1C18*1C16/3C48=1-(14*18*16)/(48!/(3!*45!)=

=1-(14*18*16)/(8*47*46)=829/1081 or about 77%


I hope I am right...

Regards,

Hopeful
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 [#permalink] New post 31 Jul 2003, 11:25
Agree with 1) = 16

but 3) I think it gets to 91/282
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 [#permalink] New post 31 Jul 2003, 12:23
You are right. #3 does get to 91/282
  [#permalink] 31 Jul 2003, 12:23
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