Most Stringent Bounds on Aggregated Probabilities of Partially Specified Dependent Probability Systems

Analysis of dependent probability systems of a moderate to large finite number (m) of events must often be based solely on the partial system information given by S 1, the sum of the probabilities of occurrence of the m individuaf events; and S 2, the sum of the probabilities of occurrence of each of the ( m 2) pairs of events. This information is used to develop the most stringent upper and lower bounds on the aggregated probabilities P [n], the probability of occurrence of exactly n events (n = 0, 1, …, m); and on P 1, the probability of occurrence of one or more of the m events. The most stringent bounds on P [m] and P 1 are more stringent than corresponding bounds presented in the literature, for most systems.