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Matching Socks

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.


Puzzle ID:#14164
Fun:*** (2.76)
Difficulty:*** (2.13)
Submitted By:mathemagicianus****




Mismatched Joe is in a pitch dark room selecting socks from his drawer. He has only six socks in his drawer, a mixture of black and white. If he chooses two socks, the chances that he draws out a white pair is 2/3. What are the chances that he draws out a black pair?


Three pairs of matching socks... maybe not!!!

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Aug 29, 2003

Aug 29, 2003

Mar 03, 2004

Actually, your answer is wrong. 45 White socks and 10 black socks also allows for a 2/3 chance of drawing a white pair. I am sure there are others.
Apr 11, 2004

Aug 01, 2004

That may be, jamesernst, but he said six socks. That leaves only the 5-1 distribution.
Nov 23, 2004

Excellent question (and it is the right answer.)
May 16, 2005

Good one!
Really fun.
Mar 05, 2006

On the other hand he could have had -4 white socks and 10 black socks in his drawer. Probability of drawing a white sock = -4/6. That would now make -5 white socks in the drawer. Probability of drawing another white sock is -5/5. Therefore the probability of drawing 2 white socks = (-4/6)x(-5/5) = 2/3. See it works! Then the probability of drawing
2 black socks is (10/6)x(9/5) = 3 Doh! I think if you draw out a negative white sock, the number of socks in the drawer increases Seriously good teaser even if I did start solving huge equations to get it!
Nov 19, 2006

Jimbo, try being a little more ... realistic?
Aug 19, 2008

i think the question is wrong
i have seen a similar question else where.., a pair of socks consists of a left sock and a right sock. (if i'm right)
u can never have a prob of 2/3 of picking a pair of white socks from six socks
Aug 25, 2008

sry for the above comment..
just thot there will be two kinds of sox...
Jan 26, 2010

Took me about 2 minutes because I started thinking about combinations like 6 choose 2 is 15, so out of these 10 has to be white pairs, and then became stumped for a bit.

Then I realized probably of drawing 2 whites is just x/6 * (x-1)/5 with x being the number of white socks. Sigh I wish I could get the insight to just get to this step in the first place -_-
Sep 11, 2010

Haha the me 7 months ago sure was dumb. You can do this easily w/ combinations as well. The key is to note the number of white socks choose 2 must equal 10 on the numerator. Hence, there are 5 white socks.
Apr 27, 2011

Loved it!!!!
Didn't solve it though

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