A Variant of Banach's Match Box Problem

Abstract

Publisher Summary Sampling from a certain simple bipartite graph is shown to lead to some interesting combinatorial and statistical problems. A basic probability distribution can be derived from simple arguments without invoking. A picturesque formulation of the graph sampling scheme in terms of pills taken from a medicine bottle is reminiscent of the classical match box problem discussed in the chapter. Certain parallels which can be exploited, exist between the two processes: on the one hand that of taking matches from a match box, on the other that of choosing pills from a medicine bottle. The chapter briefly explains medicine bottle problem. A medicine bottle contains a total of N double-strength sleeping pills. These pills can easily be divided in half.