A lower bound on the probability of a finite union of events

AbstractA new lower bound on the probability P(A1∪⋯∪AN) is established in terms of only the individual event probabilities P(Ai)'s and the pairwise event probabilities P(Ai∩Aj)'s. This bound is shown to be always at least as good as two similar lower bounds: one by de Caen (1997) and the other by Dawson and Sankoff (1967). Numerical examples for the computation of this inequality are also provided