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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]
• Probability= 4/15

Total combination for selection of 2shoes from 16 shoes will be 16C2 and combination of selecting one left shoe of black will be 4c1 and one right of black will be 4c1, and same for brown also that will be left brown 4c1 and right brown 4c1.so remove one shoe of a color then probability will be 4/16= 1/4 and next shoe probability will be 4/15.

• One additional precision (mentiooned by one participant): there is NO "unicity" in the shoes (i.e. all right shoes of same color are identical between them, and so for all the left shoes of same color

• Thanks Mark. My comment to you via email

• Thanks Sona for your prompt reply. I answer you by email

• color 50%  specific color 50%. 2 of same color 25% LL/R 50%  L+R 12.5%

• Thanks Jim. I have asnwered you via email

• OK, it's time to publish the right (and official) answer.

The probability can be computed as a combined probability.

First, selecting the first shoe among the 16 (total of 8 pairs) : that’s 100% to be right!

Second: select the suited second shoe.

There are 15 shoes left.

The number of chance to be select a shoe that fit is 4/15

In effect, if the first shoe is black and is a left side: there are in the pile still 4 shoes that are black and right side!

The same conclusion can be made if the first shoe is black and is a right side etc…

Combined probability = 100% * 4/15 = 26.7%

Congratulation to the ones having solved this enigma. And big applause to our 4 first winners:

1. Martin WALKER - ADI - Staff Field Application Engineer, Burnham, UK

2. Gaetano PIARINO - ADI - Key Account Manager, Milan, Italy

3. Jeff EVANKO - ADI - Key Account Manager, Cleveland (OH), USA

4. Mark CEE- ADI - Snr Systems Integration Engineer, Calabarzon, Philippines

Stay tuned for the next challenge!

Regards

on Feb 20, 2023 10:20 AM

4/15 or 27%

• Out of the 15 remaining shoes, only 4 would be of same colour and other foot.
So, probability = 4/15

• Bingo Bobby! You get it! Congratulations!