A Look at P(X > Y ) in the Binomial Case

In this article we consider P(X > Y ) for two inde- pendent random variables X » B(n + m; p1) and Y » B(n; p2). This is a useful measure in biomedical studies and engineering re- liability. The calculation of this probability is discussed by using a combinatorial identity and the approximate value of that is given when n is large. Finally some special cases are discussed.