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Banach Matchbox Problem

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show
sample paths
histogram
probabilities
matches
40
seed
1
A smoker has two matchboxes, one in the left pocket and one in the right pocket, with each box initially containing
N
matches. The smoker selects a box at random each time he lights a new cigarette, and the problem is to calculate the probability that, when the smoker first discovers that the box he has just selected is empty, there are exactly
r
matches in the other box (
r=0,1,2,…,N
).
This Demonstration shows
• simulated sample paths of the numbers of matches in the two boxes
• histograms of the number of matches left in the other box
• exact probabilities of the number of matches left in the other box.
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