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A student is asked to pick marbles from a bag that contains

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linau1982
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A student is asked to pick marbles from a bag that contains [#permalink] New post   Updated on: 22 Mar 2013, 03:53
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A student is asked to pick marbles from a bag that contains 18 marbles. Eight marbles are red, 4 are green, and 6 are black. What is the minimum number of marbles that a blindfolded student would have to draw from the bag to be certain of having at least three marbles of the same color?

A. 5
B. 6
C. 7
D. 13
E. 14
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C

Originally posted by linau1982 on 03 Nov 2008, 08:18.
Last edited by Bunuel on 22 Mar 2013, 03:53, edited 1 time in total.
Edited the question and added the OA.
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Re: A student is asked to pick marbles from a bag that contains [#permalink] New post   22 Mar 2013, 04:11
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linau1982 wrote:
A student is asked to pick marbles from a bag that contains 18 marbles. Eight marbles are red, 4 are green, and 6 are black. What is the minimum number of marbles that a blindfolded student would have to draw from the bag to be certain of having at least three marbles of the same color?

A. 5
B. 6
C. 7
D. 13
E. 14


The worst case scenario would be if we remove 2 marbles of each color, so 6 marbles, and we still won't have 3 marbles of the same color. The 7th marble will be red, green or black, thus after 7 draws we are guaranteed to have at least three marbles of the same color.

Answer: C.

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A student is asked to pick marbles from a bag that contains [#permalink] New post   31 May 2018, 11:47
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Took a while to understand the question. But here's a simplified version of the question stem for those who are struggling to understand why 17 is not the correct answer.

The question simply asks after how many tries when will the student have atleast three marbles of the same colour.
If he is lucky then he can pick 3 of same colour (red, green or black) in the first three tries. This is the best case.

In the worst case, he draws them in the below order:

RRGGBBR (on the 7th he picks a red making it atleast three of same colour)
Likewise, there can be several other orders in which he may draw them i.e. GGBBRRG, BBRRGGB, BRBRGGB, BRGBGRB and so on.

Essentially, when the student draws 7 marbles there would be atleast 3 marbles of the same colour.
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Re: A student is asked to pick marbles from a bag that contains [#permalink] New post   11 Nov 2022, 03:01
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sv2023 wrote:
Bunuel why wouldnt we have 8+6+3 as the ans? The person can also pick all red balls continuously and then all blacks and then the last three of green?


We need the minimum number of marbles to guarantee that we have at least three marbles of the same color.

So, 8 + 6 + 3 = 17 cannot be an answer because we can guarantee the desired outcome in 7 (17 is not minimum).

You cannot guarantee the desired outcome in less than 7 picks because as I said in the solution above we can have a case when we pick 2 marbles of each color, so 6 marbles, and we still won't have 3 marbles of the same color.

But for 7 draws, there does not exist a case when after the 7th draw we don't have at least three marbles of the same color. That's why 7 is an answer.


Check other Worst Case Scenario Questions from our Special Questions Directory to understand the concept better.

Hope it helps.
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Re: PS [#permalink] New post   03 Nov 2008, 08:50
I think the answer is (C) 7. Because at worst case the student can draw 2 from each color and still he has to draw at least one more marble so that the third one of any color will constitute a color with three marbles.

What is OA?
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Re: PS [#permalink] New post   03 Nov 2008, 08:57
i get 7...he takes out 2 of each..so the 7th one will be of the 3rd color
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Re: PS [#permalink] New post   03 Nov 2008, 09:26
you all are right, it is 7

although, i really have hard time understanding why??? What if he keeps taking red ones... Or minimum no means that he's "lucky", keeps pulling different color each time
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Re: PS [#permalink] New post   03 Nov 2008, 11:28
linau1982 wrote:
you all are right, it is 7

although, i really have hard time understanding why??? What if he keeps taking red ones... Or minimum no means that he's "lucky", keeps pulling different color each time


What you are saying is right for the best case. However, in order to be certain, worst case has to be considered.
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Re: A student is asked to pick marbles from a bag that contains [#permalink] New post   22 Mar 2013, 03:04
It should b R+G+B and then again R+G+B and then on 7th draw,he might pick either of R/G/B thus satisfying our condition.
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Re: A student is asked to pick marbles from a bag that contains [#permalink] New post   22 Mar 2013, 03:33
The answer is 7.

There is no way we can have 7 marbles without picking at least 3 of the same color, infact we cannot write 7 as the combination of only 2 marbles of the same color:

\(2G+2B+2R+1?=7\) marbles

The last one that is missing must be G or B or R so we have at LEAST 3 of a color.
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Re: A student is asked to pick marbles from a bag that contains [#permalink] New post   04 Aug 2019, 04:59
linau1982 wrote:
A student is asked to pick marbles from a bag that contains 18 marbles. Eight marbles are red, 4 are green, and 6 are black. What is the minimum number of marbles that a blindfolded student would have to draw from the bag to be certain of having at least three marbles of the same color?

A. 5
B. 6
C. 7
D. 13
E. 14


7 (worst case(2+2+2) +1)
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Re: A student is asked to pick marbles from a bag that contains [#permalink] New post   10 Nov 2022, 20:58
Bunuel why wouldnt we have 8+6+3 as the ans? The person can also pick all red balls continuously and then all blacks and then the last three of green?
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Re: A student is asked to pick marbles from a bag that contains [#permalink] New post   13 Dec 2023, 09:43
Hello from the GMAT Club BumpBot!

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Re: A student is asked to pick marbles from a bag that contains [#permalink]
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