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

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Manager
Joined: 12 Oct 2008
Posts: 69
A student is asked to pick marbles from a bag that contains  [#permalink]

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Updated on: 22 Mar 2013, 02:53
16
00:00

Difficulty:

25% (medium)

Question Stats:

69% (01:14) correct 31% (01:39) wrong based on 308 sessions

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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

Originally posted by linau1982 on 03 Nov 2008, 07:18.
Last edited by Bunuel on 22 Mar 2013, 02:53, edited 1 time in total.
Edited the question and added the OA.
##### Most Helpful Expert Reply
Math Expert
Joined: 02 Sep 2009
Posts: 65184
Re: A student is asked to pick marbles from a bag that contains  [#permalink]

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22 Mar 2013, 03:11
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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Hope it helps.
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##### General Discussion
Manager
Joined: 11 Apr 2008
Posts: 187
Re: PS  [#permalink]

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03 Nov 2008, 07:50
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]

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03 Nov 2008, 07:57
i get 7...he takes out 2 of each..so the 7th one will be of the 3rd color
Manager
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Re: PS  [#permalink]

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03 Nov 2008, 08:26
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]

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03 Nov 2008, 10:28
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.
Manager
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Posts: 152
Re: A student is asked to pick marbles from a bag that contains  [#permalink]

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22 Mar 2013, 02:04
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]

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22 Mar 2013, 02:33
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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A student is asked to pick marbles from a bag that contains  [#permalink]

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31 May 2018, 10:47
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]

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04 Aug 2019, 03:59
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)
Re: A student is asked to pick marbles from a bag that contains   [#permalink] 04 Aug 2019, 03:59

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

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