In the Banach matchbox problem, find the probability that

Chapter 4, Problem 77P

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QUESTION:

Problem 77P

In the Banach matchbox problem, find the probability that at the moment when the first box is emptied (as opposed to being found empty), the other box contains exactly k matches.

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QUESTION:

Problem 77P

In the Banach matchbox problem, find the probability that at the moment when the first box is emptied (as opposed to being found empty), the other box contains exactly k matches.

ANSWER:

Solution

Step 1 of 1

We have to find the probability that when the first box is emptied the other box contains exactly k matches

Let X be the k matches remaining in the other box

Let E1 be the event that left hand match box is empty and k matches in the right hand box

Here  p=1/2,   r=N,    n=2N-k

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