You are in your friend's home.You are asked by your friend,
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?

There doesn't seem to be a single solution here. Consider:

if there are 3 black socks and 1 white sock in the drawer, then the probability of drawing a pair of black socks is indeed 1/2, and the probability of drawing a pair of white socks is of course zero since there's only the one.

But if there are 35 white socks and 85 black socks (120 total), then the probability of drawing a pair of black socks is still 1/2, and now the probability of drawing a pair of white socks is 1/12.

The next solution appears to be 1189 white socks and 2871 black socks which still has the desired 1/2 probability of a pair of blacks, but now has a probability of 3/35 for a a pair of whites, although certainly MY sock drawer isn't big enough for 4000+ socks :)

There seems to be an infinite number of solutions, whose probability as the total sock count grows tends to 1 / (6 + 4√2)

All of that being said, this seems a bit complex for a D2, so I think perhaps I've missed something...

Posted by Paul on 2015-09-29 11:59:43