Document Zbl 1448.60026

On bounds for probabilities of combinations of events, the Jordan formula, and the Bonferroni inequalities. (English. Russian original) Zbl 1448.60026

Vestn. St. Petersbg. Univ., Math. 52, No. 2, 178-186 (2019); translation from Vestn. St-Peterbg. Univ., Ser. I, Mat. Mekh. Astron. 6(64), No. 2, 253-264 (2019).

Summary: This paper presents a method for deriving optimal lower and upper bounds for probabilities and conditional probabilities (given a \(\sigma \)-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.

Cited in 1 Document

MSC:

60C05	Combinatorial probability
60E15	Inequalities; stochastic orderings

Keywords:

Bonferroni inequalities; Jordan formula; probabilities of combinations of events; probabilities of occurrence of several events

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References:

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