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"Select matching shoes": Why isn't the probability of the first show 1/20?

Link

http://gre.magoosh.com/questions/834

 

Question

Why isn't the probability of the first shoe 1/20?

 

Answer

The probability of the 1st shoe isn't 1/20 because the question is not asking for you to choose any particular shoe. So if you look at it this way, the probability of getting the correct shoe is 1, because any shoe you choose as the first shoe will be the correct shoe. The probability of the second shoe is 1/19 because you now have 19 shoes left after picking the first shoe. But in this case, only ONE shoe can be the correct shoe, because it must match the first one. If the questions asked for the probability of picking one specific pair of shoes, the answer would be 2/20 (because there are two shoes in the specific pair we want) multiplied by 1/19.

 

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