# Banach Matchbox Problem

Banach Matchbox Problem

A smoker has two matchboxes, one in the left pocket and one in the right pocket, with each box initially containing 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 matches in the other box ().

N

r

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.