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

In summary, the conversation is about finding the probability of drawing all 10 white balls from a box containing 10 black and 10 white balls. The experiment is repeated 20 times and the sample space is shown in an image. The solution involves using combinations and the answer is the reciprocal of the number of possible combinations. One person suggests using a tree diagram while the other is looking for a formula.
  • #1
mr_k
9
0
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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  • #2
The answer is the reciprocal of the number of possible combinations.
 
  • #3
Hi
i need to find a formula for this.
 
  • #4
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.
 
  • #5
HI
The result is not important i need a formula.
 

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

1. What is the "Hard problem" in relation to white and black balls?

The "Hard problem" refers to a thought experiment in which a person is presented with a bag containing white and black balls, and they are asked to determine the underlying rule for which balls are placed in the bag. This problem is considered "hard" because there is no way to definitively prove the rule without additional information.

2. Is there a solution to the "Hard problem"?

No, there is no definitive solution to the "Hard problem." Since the person is only given a limited number of observations, they can only make assumptions about the underlying rule. These assumptions may or may not be correct, and there is no way to prove them without additional information.

3. How does the "Hard problem" relate to the philosophy of science?

The "Hard problem" is often used as an example to illustrate the limitations of the scientific method. It shows that even with careful observation and experimentation, there may still be unanswered questions or uncertainties in our understanding of the world.

4. Can the "Hard problem" be solved with advanced technology or techniques?

No, the "Hard problem" is not a matter of lacking technology or techniques. It is a fundamental limitation of our ability to fully understand complex systems and their underlying rules. Advanced technology and techniques may help us to make more accurate observations, but they cannot definitively solve the problem.

5. What can we learn from the "Hard problem"?

The "Hard problem" reminds us that there are limitations to our understanding and knowledge, and that we must always be open to the possibility of new information or perspectives that may challenge our assumptions. It also highlights the importance of critical thinking and humility in the pursuit of scientific knowledge.

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