摘要: In a previous paper 1988, the author proposed methods to obtain sharp lower and upper bounds for probabilities that at least one out of n events occurs, based on knowledge some binomial moments number which occur linear programming formulations. This presents further results concerning other more general logical functions events: We give that: exactly r events, b occur, using programming. The basic facts are expressed by dual feasible basis characterization theorems interpreted in terms vertices problems. mention inequalities, among moments, generalize theory case nonconsecutive present numerical examples.