### Brain Teasers

# Matching Socks

Probability
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?

### Hint

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

COOL!

COOL!

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.

WRONG ANSWER

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

Excellent question (and it is the right answer.)

Good one!

Really fun.

Really fun.

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!

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!

Jimbo, try being a little more ... realistic?

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

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

sry for the above comment..

just thot there will be two kinds of sox...

just thot there will be two kinds of sox...

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 -_-

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 -_-

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.

Loved it!!!!

Didn't solve it though

Didn't solve it though

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