Banach's match-box problem: The person carries two boxes of matches, one in his left and one in his right pocket. At first they comprise N number of matches each. When the person wants a match, a pocket is chosen at random, the successive choices therefore constituting Bernoulli trials with p = ½. On the ?rst occasion which the person ?nds that the box is empty the other box might contain 0; 1; 2; ... ;N matches. Then the probability distribution of the number of matches, R, left in the other box can be given as:
So, for instance, for N = 50 the probability of there being no more than 10 matches in the second box is given by 0.754