Left and right are not the same!!!

Probability Level 2

You have 13 socks of red colour, 5 socks of blue colour ,8 socks of green colour and 10 socks of yellow colour. What is the minimum number of socks needed to ensure you have atleast 3 socks of different colour. You draw socks at random.

Inspiration left and right are the same

Try similar question by me

This question is kinda original


The answer is 24.

Aryan Sanghi by Aryan Sanghi , 17, India

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2 solutions

Why 23 23 socks won't work?

With 23 23 socks, it is possible to have 13 13 red socks of and 10 10 yellow socks.

Why 24 24 socks work?

With 24 24 socks, there are always 3 3 socks having different colors.

Hence, the smallest number of socks you must take out of the drawer in order to be certain that you have a pair that match is 24 \boxed{24} .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Excellent solution Vinayak.

Aryan Sanghi - 1 year ago

Try my new probability question here . It is not similar.

Aryan Sanghi - 1 year ago
Mahdi Raza
Jun 2, 2020

Starting from the maximum worst-case scenario, you can have all 13 red socks and all 10 yellow socks. But the 24th sock you pick will be of a different colour, which will guarantee 3 socks of different colours.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Excellent solution Mahdi. Thanks for sharing.

Aryan Sanghi - 1 year ago

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Thanks, Aryan. I can see you are coming up with variation from a single problem and that is excellent!!

Mahdi Raza - 1 year ago

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Thanks a lot @Mahdi Raza .

Aryan Sanghi - 1 year ago

Try my new probability question here . It is not similar.

Aryan Sanghi - 1 year ago

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