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In his pocket, a boy has 3 red marbles, 4 blue marbles, and

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In his pocket, a boy has 3 red marbles, 4 blue marbles, and [#permalink] New post 12 Oct 2009, 11:40
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In his pocket, a boy has 3 red marbles, 4 blue marbles, and 4 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?

A. 3
B. 7
C. 8
D. 9
E. 11
[Reveal] Spoiler: OA

Last edited by Bunuel on 02 Nov 2012, 13:11, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Probability question [#permalink] New post 12 Oct 2009, 12:05
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timmaxwell8 wrote:
24. In his pocket, a boy has 3 red marbles, 4 blue marbles, and 4 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?

A. 3
B. 7
C. 8
D. 9
E. 11


The worst scenario would be that he has taken 4 blue and 4 green, total of 8 marbles, and still doesn't have 3 distinct colors. But the next draw (9th) will surely be the third color red as there is no other color marble left in pocket.

Answer D (9)
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Re: Probability question [#permalink] New post 12 Oct 2009, 20:16
I think, the only way to figure out this problem is just to use logic, just as Bunuel did.
I do not see any other solution for that.
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Re: Probability question [#permalink] New post 14 Oct 2009, 03:52
I agree...only logic will help

take out 4G + 4B + 1R = 9 marbles
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Re: Probability question [#permalink] New post 06 Jun 2010, 17:39
What about scenario of choosing 3 red and 4 blue and still seeing distinct color.
In other words why can't we have 8 marbles drawn and still see three distinct colors? 3red+4 blue=7 marbles and on 8th draw should be green since remaining should be all green marbles?

Can someone please explain why?

Thanks in advance.
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Re: Probability question [#permalink] New post 06 Jun 2010, 19:02
srichaks wrote:
What about scenario of choosing 3 red and 4 blue and still seeing distinct color.
In other words why can't we have 8 marbles drawn and still see three distinct colors? 3red+4 blue=7 marbles and on 8th draw should be green since remaining should be all green marbles?

Can someone please explain why?

Thanks in advance.


The word "ensure" in the question basically is asking in the worst case scenario. So yes technically, the scenario outlined above is true as well, it is not the worst possible outcome.

In order to guarantee the outcome of one of each color, you need to take into account all of the balls in the two largest groups which equals 8.

Hope that helped.
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Re: In his pocket, a boy has 3 red marbles, 4 blue marbles, and [#permalink] New post 26 Sep 2013, 04:01
What is the difference between this question and the one below.Please explain its confusing:

There are 15 black chips and 5 white chips in a jar. What is the least number of chips we should pick to guarantee that we have 2 chips of the same color?
A. 3
B. 5
C. 6
D. 16
E. 19

Worst case scenario would be if the first two chips we pick will be of the different colors. But the next chip must match with either of two, so 3 is the answer.

Answer: A.
Re: In his pocket, a boy has 3 red marbles, 4 blue marbles, and   [#permalink] 26 Sep 2013, 04:01
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