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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)
Category:Probability
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?



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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