Socks in th Dark

Probability Level 1

10 black socks, 8 white socks, and 3 blue socks are in your drawer. The room is pitch dark. If you take socks out one at a time, how many socks might you need to remove until you can be sure that you're holding at least two socks of the same color?

3 8 4 21 (all of them)

Zandra Vinegar by Zandra Vinegar

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5 solutions

Harshi Singh
Aug 16, 2015

since there are only 3 kinds of socks namely black white and blue. if you randomly take them , after taking 3 atleast of one each variety then at the next no matter which sock you take ......you have 2 of same color

6 Helpful 0 Interesting 0 Brilliant 0 Confused

I don't think so , What if you take 3 or upto 10 Sockes and all are black ? , so I believe answer would be 11 in this case, considering wrost case.

Ashish Sheth - 5 years, 10 months ago

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When you are taking out all 10 black socks, don't you think you have already got a matching pair of black? When we take out 4 socks, even in the worst case we will get 1st three of different colours but the 4th sock has to match one of the existing 3 socks as there are only 3 colours. So minimum number we need to remove to make sure we have got a matching pair is 4.

Kushagra Sahni - 5 years, 10 months ago

You need 11 socks if you're looking for two differently-colored socks.

Ivan Koswara - 5 years, 9 months ago
Ishan Mishra
Aug 21, 2015

The worst case scenario is that you take out 3 socks, and each of them is a different colour- one black, one white, and one blue.

But the next time you withdraw a sock, regardless of the colour that comes out, you will have two socks of the same colour!

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Hadia Qadir
Aug 30, 2015

4, but you'll still have to turn the lights on to work out which two make a pair.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Dev SAini
Aug 21, 2015

When we taken out socks one by one in worst condition up to 3 chances all are different then in 4 time one socks will be match to previous one . So we need 4 attempt to sure that we have two socks of same color.

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Vaibhav Sahu
Aug 21, 2015

A simple case of the Pigeonhole Principle.

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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