Minimum numbers of balls to be drawn

In summary, the conversation discusses the minimum number of balls that must be drawn, without replacement, to ensure getting a specific number of each color ball from a box containing 20 red, 30 black, 40 blue, and 50 white balls. The solution involves understanding the concept and reasoning rather than using a formula, and it is determined that at least 120 balls must be drawn to be certain of obtaining at least one red ball.
  • #1
usha
11
0

Homework Statement


suppose in a box there are 20 red, 30 black,40 blue,and 50 white balls.what is the minimum numbers of balls to be drawn, without replacement,so that you are certain about getting 4 red, 5 black, 6 blue and 7 white balls?

Homework Equations

The Attempt at a Solution


so there are total 140 balls and i have to get 22 balls with the following configuration. i tried to use this formula..
[(40C6)(20C4)(30C5)(50C7)]/(140C22)
but i am not sure... i think this gives the probability of getting this configuration... but for minimum balls to be drawn... i don't know which formula can be used...
 
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  • #2
Forget the formulas and use your understanding.
The key is that you have to be certain of those numbers...
 
  • #3
With 140 balls and 20 red balls, how many must you draw to be certain that you will have at least one red ball?
It is probably more than 120, since there is at least one way to pull 120 non-red balls.
 

1. What is the minimum number of balls that need to be drawn from a bag to guarantee a match?

The minimum number of balls that need to be drawn from a bag to guarantee a match is equal to the total number of different types of balls in the bag plus one. This is known as the pigeonhole principle.

2. Can the minimum number of balls to be drawn vary depending on the bag's contents?

Yes, the minimum number of balls to be drawn can vary depending on the bag's contents. It is determined by the number of different types of balls in the bag.

3. How does the number of balls in the bag affect the minimum number of balls to be drawn?

The number of balls in the bag does not affect the minimum number of balls to be drawn. The minimum number of balls to be drawn is solely determined by the number of different types of balls in the bag.

4. Is the minimum number of balls to be drawn the same as the maximum number of balls to be drawn?

No, the minimum number of balls to be drawn is not necessarily the same as the maximum number of balls to be drawn. The minimum number guarantees a match, while the maximum number may not.

5. Can the minimum number of balls to be drawn be calculated using a formula?

Yes, the formula for calculating the minimum number of balls to be drawn is n + 1, where n is the number of different types of balls in the bag.

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