On Bounds for Probabilities of Combinations of Events, the Jordan Formula, and the Bonferroni Inequalities
This paper presents a method for deriving optimal lower and upper bounds for probabilities and conditional probabilities (given a σ-field) for various combinations of events. The optimality is understood as the possibility that inequalities become equalities for some sets of events. New generalizations of the Jordan formula and the Bonferroni inequalities are obtained. The corresponding conditional versions of these results are also considered.
KeywordsBonferroni inequalities Jordan formula probabilities of combinations of events probabilities of occurrence of several events
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The author is grateful to anonymous reviewers, whose comments favored the improvement of the text of this paper.