Beyond Inclusion-and-Exclusion: Natural Identities for P[Exactly t Events] and P[at Least t Events] and Resulting Inequalities
Fred M. Hoppe · International Statistical Review · 1993
Summary We present universal identities for the probability of occurrence of at least t, or exactly t, out of n arbitrary events. Well-known, as well as new, bounds can be derived simply from these identities. The approach is probabilistic and provides a natural and unified approach to these inequalities. It also has the advantage of showing how these relationships are consequences of two elementary results: P(AB) = P(A) - P(AB); and P(E) > P(F) if E D F.