Number of Marbles to be Removed?

  • Thread starter zak100
  • Start date
In summary, if you remove marbles one at a time, randomly, and want to be sure that you have at least 2 marbles of each color, you must remove at least 14 marbles.
  • #1
zak100
462
11

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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  • #2
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.
 
  • #3
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:
  • #4
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.
 
  • #5
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:
 
  • #6
"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).
 
  • #7
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 ...
 
  • #8
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)
 

1. How do you determine the optimal number of marbles to be removed?

The optimal number of marbles to be removed is determined through mathematical analysis and statistical modeling. Factors such as the total number of marbles, the desired outcome, and the rules of the game are taken into consideration.

2. Can the optimal number of marbles to be removed change based on different game scenarios?

Yes, the optimal number of marbles to be removed can change based on different game scenarios. Factors such as the total number of marbles, the desired outcome, and the rules of the game can all affect the optimal number.

3. Is there a specific formula for calculating the optimal number of marbles to be removed?

There is no one specific formula for calculating the optimal number of marbles to be removed. It often involves a combination of mathematical analysis and statistical modeling, and may vary depending on the specific game and its rules.

4. How does the number of marbles to be removed affect the outcome of the game?

The number of marbles to be removed can greatly impact the outcome of the game. Removing too many or too few marbles can lead to an unfavorable outcome, while removing the optimal number can increase the chances of winning.

5. Are there any strategies for determining the optimal number of marbles to be removed?

There are various strategies that can be used to determine the optimal number of marbles to be removed, such as trial and error, mathematical calculations, and game theory. Ultimately, the best strategy will depend on the specific game and its rules.

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