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In the problem known as Banach's matchbox (original problem given below) what would be the case if the question did not mention the fact "it is equally likely that he will reach either pocket"??

Banach's matchbox problem: Suppose a mathematician carries two matchboxes at all times: one in his left pocket and one in his right. Each time he needs a match, he is equally likely to take it from either pocket. Suppose he reaches into his pocket and discovers for the first time that the box picked is empty. If it is assumed that each of the matchboxes originally contained n matches, what is the probability that there are exactly k matches in the other box?

Jean-Claude Arbaut
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taha entesari
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1 Answers1

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Without that definition the problem is not solvable. It could be that he always reaches into the left pocket. In that case when he runs out of matches there are still $n$ in the right pocket. In that case the probability of $n$ is $1$ and the probability of any other number is $0$. If he picks randomly and $n$ is a little large, the chance that there are $n$ left when he runs out is very small.

Ross Millikan
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