A lower bound on the probability of a finite union of events (Q1974530)

The aim of the paper is to obtain a new lower bound on the probability \(P(A_1\cup\cdots\cup A_n)\) in terms of only the individual event probabilities \(P(A_i)\), \(i=1,2, \dots,n\), and the pairwise event probabilities \(P(A_i\cap A_j)\), \(i,j=1,2, \dots,n\). The provided formula is shown to be always at least as good as other two similar, previously obtained lower bounds, since these ones are proved to be particular cases of the authors' formula. Two numerical examples illustrate the improved lower bound for \(P(A_1\cup \cdots\cup A_n)\).