You are in a pitch black room and need to get a pair of socks out of your drawer which can contain up to 100 socks. In the drawer is a mixture of black and white socks, and there's at least one pair of either color. If you choose two socks, the chance that you draw out a black pair is 2/3.

What is the chance that you draw out a white pair?
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Bonus: what would the answer be if the drawer contained between 100 and 1000 socks?

(In reply to Solution (maybe) by Nate)

Hey Nate -

First, did you mean to post 3 times, or maybe just hit the submit button too many times?  Not important... =)

Second, the probability of drawing a black pair isn't quite he probability of drawing one black sock squared.  Remember, you removed the first black, so there is one less black sock AND one less sock in the total.

So your probability is actually B/(B+W)  (the probability of pulling the first black sock) times (B-1)/(B+W-1)  (the probability of pulling another black sock after you already removed one, out of the total number of socks left after removing one).

I hope that helps!

Posted by nikki on 2004-09-03 15:54:59