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

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03 Nov 2008, 08:18

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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?

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.

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

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.

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

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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. _________________

It is beyond a doubt that all our knowledge that begins with experience.

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

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22 Mar 2013, 04:11

Expert's post

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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.

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