Conditional probability: Difference between revisions

Revision as of 18:54, 6 November 2022

Revision as of 19:55, 14 November 2022

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

This equation for a conditional probability, although mathematically equivalent, may be intuitively easier to understand. It can be interpreted as "the probability of ''B'' occurring multiplied by the probability of ''A'' occurring, provided that ''B'' has occurred, is equal to the probability of the ''A'' and ''B'' occurrences together, although not necessarily occurring at the same time". Additionally, this may be preferred philosophically; under major [[probability interpretations]], such as the [[Subjective probability|subjective theory]], conditional probability is considered a primitive entity. Moreover, this "multiplication rule" can be practically useful in computing the probability of <math>A \cap B</math> and introduces a symmetry with the summation axiom for [[mutuallyPoincaré exclusive events]]Formula:<ref>Gillies, Donald (2000); "Philosophical Theories of Probability"; Routledge; Chapter 4 "The subjective theory"</ref>

:<math>P(A \cup B) = P(A) + P(B) - P(A \cap B)</math>