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# A jar contains 20 marbles: 4 red, 6 white and 10 blue

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A jar contains 20 marbles: 4 red, 6 white and 10 blue [#permalink]  06 Nov 2016, 13:11
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A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove marbles one at a time, randomly, what is the minimum number that must be removed to be certain that you have at least 2 marbles of each colour?

A. 6
B. 10
C. 12
D. 16
E. 18
[Reveal] Spoiler: OA
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Re: A jar contains 20 marbles: 4 red, 6 white and 10 blue [#permalink]  06 Nov 2016, 13:40
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Expert's post
Here we have 10 Blue 6 White and 4 Red. The worst case scenario you pull all white and blue before you pull 2 red.

Hence minimum number of marbles you need the pull is all 10 white, 6 White and 2 Red.

Number of marbles to be removed = $$10 + 6 + 2$$ = $$18$$
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Re: A jar contains 20 marbles: 4 red, 6 white and 10 blue [#permalink]  06 May 2018, 16:39
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SJ wrote:
A jar contains 20 marbles: 4 red, 6 white and 10 blue. If you remove marbles one at a time, randomly, what is the minimum number that must be removed to be certain that you have at least 2 marbles of each colour?

A. 6
B. 10
C. 12
D. 16
E. 18

Assume the worst case scenario, that is, you remove all 10 blue marbles and all 6 white marbles; you still don’t have any marbles in red. However, if you remove 2 more marbles (and they must be red), then you will have at least 2 marbles of each color. Therefore, you need to remove a total of 18 marbles to ensure you will have at least 2 marbles of each color.

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Jeffery Miller

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Re: A jar contains 20 marbles: 4 red, 6 white and 10 blue [#permalink]  22 Aug 2018, 14:37
what I don't understand is why this must be a worst case scenario. the question asks for the minimum number that must be removed -- doesn't that mean best case scenario? In which case, wouldn't the answer be 4 red+6 white+2 blue = 12?
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Re: A jar contains 20 marbles: 4 red, 6 white and 10 blue [#permalink]  22 Aug 2018, 15:51
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anabanana wrote:
what I don't understand is why this must be a worst case scenario. the question asks for the minimum number that must be removed -- doesn't that mean best case scenario? In which case, wouldn't the answer be 4 red+6 white+2 blue = 12?

The key is in the language of the question: 'the minimum number of marbles removed so that you are certain', certain being the keyword here. Now you can remove the 12 marbles as you pointed out but can you be certain that you have each kind.

Say you pick twelve: 10 blue and 2 white. Hence no red at in the selection. Hence we assume the worst case scenario.
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Re: A jar contains 20 marbles: 4 red, 6 white and 10 blue   [#permalink] 22 Aug 2018, 15:51
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