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Consider a fixed set of n events. Let S 1 denote the sum of the probabilities of occurrence of each event and S 2 the sum of the probabilities of occurrence of each of the pairs of events. Using a dual linear programming method a sharp upper bound is derived for the probability of occurrence of at least m out of the n events when S 1 and S 2 are given. The bound improves one of the inequalities obtained by Sathe et al. (1980).

Consider a fixed set of n events. Let S1 denote the sum of the probabilities of occurrence of each event and S2 the sum of the probabilities of occurrence of each of the pairs of events. Using a dual linear programming method a sharp upper bound is derived for the probability of occurrence of at least m out of the n events when S1 and S2 are given. The bound improves one of the inequalities obtained by Sathe et al. (1980).

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