Matching Socks
Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.
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?
HintThree pairs of matching socks... maybe not!!!
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Answer
He has a ZERO chance of drawing out a black pair.
Since there is a 2/3 chance of drawing a white pair, then there MUST be 5 white socks and only 1 black sock. The chances of drawing two whites would thus be: 5/6 x 4/5 = 2/3 . With only 1 black sock, there is no chance of drawing a black pair.
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Comments
jacintan
Aug 29, 2003
 COOL! 
jacintan
Aug 29, 2003
 COOL! 
jamesernst
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. 
ghost09
Apr 11, 2004
 WRONG ANSWER 
Poker
Aug 01, 2004
 That may be, jamesernst, but he said six socks. That leaves only the 51 distribution. 
tsimkin
Nov 23, 2004
 Excellent question (and it is the right answer.) 
brianz
May 16, 2005
 Good one!
Really fun. 
Jimbo
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! 
calmsavior
Nov 19, 2006
 Jimbo, try being a little more ... realistic? 
donga
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 
donga
Aug 25, 2008
 sry for the above comment..
just thot there will be two kinds of sox...

opqpop
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 * (x1)/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 _ 
opqpop
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. 
Jayo
Apr 27, 2011
 Loved it!!!!
Didn't solve it though 
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