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Chapter 4: Q.4.77 (page 169)

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 kmatches.

Short Answer

Expert verified

P(E)=2路2N-k-1N-1122N-k

Step by step solution

01

Step 1:Given information

Given in the question that,we need to find find the probability that at the moment when the first box is emptied (as opposed to being found empty), the other box contains exactly kmatches in the Banach matchbox problem.

02

Step 2:Explanation

LetEindicate the event that defines the moment when the first box is emptied, the other box holds exactly kmatches. This event will happen if and only if we make our Nthe selecting of the right-hand box at (2N-k)the trial. Using a similar argument as in Example, we have that

P(E)=2路2N-k-1N-1122N-k

The factor 2is because of the fact that the considered box is not fixed, it might be left-handed or right-handed.

03

Step 3:Final answer

P(E)=2路2N-k-1N-1122N-k

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