While a mathematical model cannot reflect all the elements of reality, modeling involves drastic simplifications, and those expounding the mathematical model would recognize the complexity of the elements. This article illuminates this cause with a mathematical model that seems to be in vogue, developed by the renowned mathematician Simeon Poisson. It reviews the Poisson model in order to enucleate its many assumptions. It also explains why these assumptions may introduce serious errors into the probabilities calculated according to the model. It also indicates one reason that even a relatively error free model would have limited usefulness in resolving the constitutional issue posed by juries composed of fewer than twelve persons.