What Is the Probability of Drawing All White Balls in This Experiment?

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Homework Help Overview

The discussion revolves around a probability problem involving drawing balls from a box containing both black and white balls. The original poster describes an experiment where balls are drawn repeatedly, and they seek to determine the probability of drawing all white balls after a series of trials.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of combinations to calculate probabilities and mention the need for a formula. Some suggest using a tree diagram to visualize the outcomes, while others express concerns about the complexity of this method.

Discussion Status

The conversation is ongoing, with participants exploring different methods to approach the problem. There is a focus on finding a formula rather than achieving a specific result, indicating a productive inquiry into the underlying concepts.

Contextual Notes

Participants note the constraints of the problem, including the requirement to use combinations and the challenge posed by the size of the sample space. The original poster also expresses uncertainty about how to proceed with the calculations.

mr_k
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HI, sorry about the english
can you help me with this question?


box initially contains 10 black balls and 10 white balls. The following experiment is repeated indefinitely 20 times : A ball is drawn from the box; if the ball is black it is put back in the box, otherwise it is left out.
what is the probability to draw out all 10 white balls?

i need solve this with combinations.
i know that have (20 k) to draw K white balls and k<=10.hence Sample space :
http://img268.imageshack.us/img268/1744/lllfm.jpg

ו don't know to continue...
thanks!
 
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The answer is the reciprocal of the number of possible combinations.
 
Hi
i need to find a formula for this.
 
Try to solve your problem using the tree diagram , and add all the probabilites of having 10 blacks ."well the tree diagram is going to be huge". but it works , I know there is another way to do that , but I am not familiar with.
 
HI
The result is not important i need a formula.
 

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