De Moivre's Poisson Approximation to the Binomial

Abstract

Summary In his first work on probability, written in 1711, Abraham De Moivre looked at the problem of finding the number of trials required in a binomial experiment to achieve a probability of 1/2 of finding at least some given number of successes. He looked at two cases: when the probability of success p = 1/2 and when p is small but n, the number of trials, is large. In the latter case, unlike other problems that he solved in probability, De Moivre never revealed his method of solution. We explore the solution that De Moivre originally suggests and find that his method does not work. We explore other numerical solutions and put forward the suggestion that De Moivre relied on a very cumbersome and tedious method of solution based on his earlier work on series in the 1690s. Since his method was neither quick nor mathematically elegant, he never revealed the method that he used to obtain his numerical solutions.