Bounds on the probability of the union and intersection of m events
- 1 June 1975
- journal article
- research article
- Published by Cambridge University Press (CUP) in Advances in Applied Probability
- Vol. 7 (02) , 431-448
- https://doi.org/10.1017/s000186780004605x
Abstract
For dependent probability systems of m events partially specified only by the quantities S 1, the sum of the probabilities of the m individual events; S 2, the sum of the probabilities of each of the (m) pairs of events and S 3 the sum of the probabilities of each of the (m 3) combinations of three events; this paper develops the most stringent upper and lower bounds on P 1, the probability of the union of the m events; and on P [m], the probability of the simultaneous occurrence of the m events.Keywords
This publication has 5 references indexed in Scilit:
- A general Poisson limit theorem of probability theoryDuke Mathematical Journal, 1973
- On Bonferroni-Type Inequalities of the Same Degree for the Probability of Unions and IntersectionsThe Annals of Mathematical Statistics, 1972
- Information Retrieval for Media PlanningManagement Science, 1968
- An inequality for probabilitiesProceedings of the American Mathematical Society, 1967
- On the application of the Borel-Cantelli lemmaTransactions of the American Mathematical Society, 1952