Duality and Symmetry in the Hypergeometric Distribution

Abstract

A CNN posting on the internet [1] reports that the 1996 trial of a rap star on manslaughter charges resulted in a hung jury. The posting says that the jury was composed of 7 men and 5 women and was hung at 9 to 3. Not reported is how many men or women voted with the majority. Several interesting probability problems come to mind. For example, what is the probability that exactly 5 jurors among the fnajority are men? The usual solution for such a problem utilizes methods that are associated with the hypergeometric probability distribution and involves designating successes and choosing a sample from a population. For the problem stated, it is clear that the population is the 12 jurors. But for the men and the majority, it is not so clear which should be et et ic istribution