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# KCC's Quizzes: Taking the right shoes in the dark and in a hurry

A pile of shoes consists of 4 pairs of black and 4 pairs of brown shoes mixed together in a box.

All the shoes belong to one same person.

What is the probability to randomly select a pair of shoes that are the same color, one left and one right ?

Good luck and Try to be among the 4 first ones!

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[edited by: emassa at 3:47 PM (GMT -5) on 6 Feb 2023]
• So as not to spoil it, I emailed you my answer.

Suppose you select a Black-Left shoe (P= 4/16=1/4), the probability to select a Black-Right shoe after that is 4/15. The joint probability is 1/15. You have same probability for all the possible "good" combinations: Black-Left + Black-Right, Black-Right+Black-Left, Brown-Right+Brown-Left, Brown-Left+Brown-Right. So the probability we're looking for is 4/15.

In the box, there are 4 left black shoes, 4 right black shoes, 4 left brown shoes and 4 right brown shoes.  There are 16 shoes total.

The chance of selecting the first shoe of the part is 100%.  Now you have 15 shoes left.  The chance of picking a pair is 4 out of 15……26.66%

• Once I choose one shoe, there are 15 left.  Three of those shoes will match, 12 will not.  So the chance of selecting a matching pair is 20%

• Arrggghh!  I didn't want a matching shoe, I needed a mate.  So 4/15 like others noted above.  Guess I had two left feet on this quiz.

• Thanks Gaetano for your prompt reply! I give my comment to you via email.

• Thanks Jeff for your prompt answer. I give my comment to you by email

• Glad to hear from you Erin! Hope everything goes well for you! I missed San Jose... For the quiz, I give my feedback to you by email.

• 4/15

For example, the first selected shoe is a black left and the remaining shoes that are black right is 4. Then the probability of picking a black right shoe from the remaining 15 shoes will be 4/15.