Number of Marbles to be Removed?

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To ensure at least two marbles of each color are removed from a jar containing 4 red, 6 white, and 10 blue marbles, a minimum of 16 marbles must be taken out. The initial assumption of 14 marbles was incorrect, as it is possible to draw without obtaining two of each color. Clarification on the problem statement indicates that "at least 2 marbles of each color" means two marbles from each color category, not just two from any single color. The discussion highlights the importance of understanding the wording in mathematical problems. Ultimately, careful consideration of the worst-case scenario is crucial for solving such problems accurately.
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Homework Statement


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 color?

Homework Equations


I don't think any eq is required

The Attempt at a Solution


I think 14 marbles must be removed. This would leave us with only 6 marbles remaining and then we can be certain that we have atleast 2 marbles of each color.
However my answer is not correct. Somebody please guide me.

Zulfi.
 
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Think about what the worst-case scenario is if the last color you have two of is red, white, or blue, respectively.

Edit: 14 is clearly too few. It is possible to draw 14 without drawing a single white.
 
Hi,

Thanks all. This is a matter of English. Question says:

at least 2 marbles of each color
Does it mean only 2 marbles of one color?

or

2 marbles of all color?

If it means only 2 marbles of one color then we have to remove 18 marbles. It does not ask for the color. So still we don't know that both the marbles removed are of same color but there is a possibility that they can be of same color.

Am i right?Zulfi.
 
Last edited by a moderator:
zak100 said:
Does it mean only 2 marbles of one color?

or

2 marbles of all color?
It is not an issue of English, the problem statement is clear. "At least 2 marbles of each colour" is quite unambiguous.

Also, please be advised that providing answers and direct solutions to homework problems is against the forum rules.
 
Orodruin said:
Also, please be advised that providing answers and direct solutions to homework problems is against the forum rules.
Turns out he's the OP... :smile:
 
"you have" refers to the marbles you take out, not the marbles that are left. If you draw just 16, you might draw all blue and all white marbles, for example. Then you don't have two red marbles (you don't have any red marble).
 
berkeman said:
Turns out he's the OP... :smile:
Weird, could have sworn I checked that... don't drink and post on PF I guess ...
 
Orodruin said:
Weird, could have sworn I checked that... don't drink and post on PF I guess ...
LOL. Wish I could say that it's never happened to me. o0)
 

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