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 to part 1 by Tristan)

I came up with the same combination of 5 black and 1 white but the problem states that "there's at least one pair of either color".  I guess there is at least one pair of "either" colour, as opposed to one pair of "each" colour".  I can see no other solution for part 1.

For a solution up to 1000 socks, I came up with 441 black and 99 white.

 

Posted by Nosher on 2004-09-01 18:01:52