number theory

Probability Level 1

If you have 30 white socks, 22 black socks, and 14 blue socks scattered across the floor in the dark, how many would you have to grab to get a matching pair?


The answer is 4.

Akash Dhasmana by akash dhasmana , 20, India

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2 solutions

The worst case scenario is to get one piece of sock on each color, there are three different colors. After getting one piece on each color, the next one will provide a matching pair. So the maximum is 4 socks.

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Sai Ram
Mar 24, 2016

The answer is clearly 4 because,

If we pick out 4 socks, if in the worst case scenario, he gets all the 3 socks as different in color, he would find the 4th sock as of the color of at least one of the colors as only 3 colors are available

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