Conditional probability: Difference between revisions

Revision as of 09:09, 17 November 2022

Revision as of 06:19, 9 December 2022

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:<math>P(B\mid A) = P(B)</math>

is also equivalent. Although the derived forms may seem more intuitive, they are not the preferred definition as the conditional probabilities may be undefined, and the preferred definition is symmetrical in ''A'' and ''B''. Independence does not refer to a disjoint event.<ref>{{Cite book|last=Tijms|first=Henk|url=https://www.cambridge.org/core/books/understanding-probability/B82E701FAAD2C0C2CF36E05CFC0FF3F2|title=Understanding Probability|date=2012|publisher=Cambridge University Press|isbn=978-1-107-65856-1|edition=3|___location=Cambridge|doi=10.1017/cbo9781139206990}}</ref>

It should also be noted that given the independent event pair [A B] and aan variableevent BC, the pair is conditional independent is defined to be [[Conditional independence|conditionally independent]] if the product holds true:<ref>{{Cite book|last=Pfeiffer|first=Paul E.|url=https://www.worldcat.org/oclc/858880328|title=Conditional Independence in Applied Probability|date=1978|publisher=Birkhäuser Boston|isbn=978-1-4612-6335-7|___location=Boston, MA|oclc=858880328}}</ref>

<math>P(AB \mid C) = P(A \mid C)P(B \mid C)</math>