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 Black and white socks (Posted on 2015-09-29)
a mathematician to enter a totally dark room and to pick up a pair of socks from a certain drawer.
You are told that there are some socks in that drawer, and that each can be either black or white.
You are told as well that the probability of picking at random two black socks is 1/2.

What is the probability of taking out a pair of white socks from the drawer?

 No Solution Yet Submitted by Ady TZIDON No Rating

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 re: Solution?? | Comment 2 of 8 |
(In reply to Solution?? by Paul)

Maybe you didn't miss something.  Maybe you found something.

When this was in the queue I assumed this problem was simple and your first solution was the only one.  I don't think I was the only one.

Instead it appears there are infinitely many solutions.

You did miss some solutions though:
The unreduced ratio of black to total socks can be any of
3/4, 15/21, 85/120, 493/697, 2871/4060...
where both the numerator an denominator follow the recursion relation a(n)=6*a(n-1)-a(n-2)-2.

See
https://oeis.org/A011900 black
https://oeis.org/A182435 total
https://oeis.org/A001109 white

 Posted by Jer on 2015-09-29 13:22:09

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