Colored Balls

Probability Level 1

In an urn, there are 25 red balls, 20 white balls and 15 black balls. Without looking at the balls or the urn, what is the minimum amount of balls that you should extract so that you are 100% sure that you have extracted at least 10 balls of the same color?

28 30 45 All of them

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Mircea Petre Bogdan by Mircea Petre Bogdan , 25, Romania

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2 solutions

We're talking about the minimum number so that we certainly have at least 10 balls of the same color. Taking into consideration the most unfortunate case, let's say we extract 27 balls. There is a slight chance we will extract 9 white balls, 9 red balls and 9 black balls. However, extracting a 28th ball would mean that we have at least 10 balls of the same color without any doubt.

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Since we are blind folded if we take even 28 we have the possibility to have taken 25 red 1 black 1 blue therefore no guarantee now if we take 45 we ensured we have taken at least 10 from each collor

Babis Papadopoulos - 4 years, 6 months ago

I agree with Babis, the question is badly phrased and it's to easy consider the problem for 10 of "all" colours as opposed to any single colour.

Derek Maltby - 4 years, 6 months ago
Varun M
Apr 16, 2016

The maximum number of balls we can extract without having 10 balls of same color is 27 ( 9 black,9 red,9 white). So when we extract the 28th ball it will lead to at least 10 balls having same color .Therefore answer is 28

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