In probability theory, Boole's inequality, also known as the union bound, says that for any finite or countable set of events, the probability that at least one of the events happens is no greater than the sum of the probabilities of the individual events. Boole's inequality is named after George Boole.
Formally, for a countable set of events A1, A2, A3, ..., we have
In measure-theoretic terms, Boole's inequality follows from the fact that a measure (and certainly any probability measure) is σ-sub-additive.
Read more about Boole's Inequality: Proof, Bonferroni Inequalities
Famous quotes containing the word inequality:
“The doctrine of equality!... But there exists no more poisonous poison: for it seems to be preached by justice itself, while it is the end of justice.... Equality for equals, inequality for unequalsMthat would be the true voice of justice: and, what follows from it, Never make equal what is unequal.”
—Friedrich Nietzsche (18441900)