Inequalities for the probability of the occurrence of at least <i>m</i> out of <i>n</i> events

Abstract

Given n events A 1 , A 2 , · ··, A n , bounds are obtained for the probability of the occurrence of at least m out of the n events. The bounds are linear in terms of S 1 and S 2 where S 1 = Σ i P ( A i ) and S 2 = Σ i&lt;j Ρ ( Α i , Α j ). The bounds are illustrated with an example. For m = 1 the bounds are the same as the best known linear bounds in terms of S 1 and S 2 .