Bounds on the probability of the union and intersection of m events

Abstract

For dependent probability systems of m events partially specified only by the quantities S 1, the sum of the probabilities of the m individual events; S 2, the sum of the probabilities of each of the (m) pairs of events and S 3 the sum of the probabilities of each of the (m 3) combinations of three events; this paper develops the most stringent upper and lower bounds on P 1, the probability of the union of the m events; and on P [m], the probability of the simultaneous occurrence of the m events.