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Probability with conditional replacement

  • Thread starter pr07
  • Start date
1
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1. The problem statement, all variables and given/known data
We have a bag of n balls, n/2 of which are green and n/2 of which are blue. Consider the following experiment: We reach into the bag and pull out two balls. If they of the same type, we put them both back in the bag. If they are of di erent types we put them both on the ground.
1. What is the probability that we put the balls on the ground?
2. What is the expected number of times we have to repeat this experiment until we get to put some ball on the ground?
3. What is the expected number of times we have to repeat this experiment before the bag is empty?


2. Relevant equations



3. The attempt at a solution
1. n/2n * n/2(n-1) + n/2n * n/2(n-1) = n/2(n-1)
2. 2(n-1)/n
1. The problem statement, all variables and given/known data



2. Relevant equations



3. The attempt at a solution
 
OK on the first two parts. For the third part, is there any reason that the expected times wouldn't be additive? I mean, whether it takes 10 tries or 1 try to remove balls n and n-1, the number of tries it will take after that to remove n-2 and n-3 should be the same.

So you can write out the sum and fiddle it down to a formula.
 

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