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| = Conditional Probability = A '''conditional probability''' is the likelihood of an event happening given that another event happens. The math notation is ''P(A|B)'', as in the probability of ''A'' given ''B''. <<TableOfContents>> ---- == Decomposition == {{attachment:decomposition.svg}} === Bayes Theorem === {{attachment:bayes.svg}} ---- == Independence == If two events are [[Statistics/Independence|independent]], then probabilities of one do not change from being conditioned on the other. Put simply, if the conditioning probability is not 0, then: ''P(A|B) = P(A)'' ''P(B|A) = P(B)'' A conditioning probability of 0 will cause the conditional probability to be undefined. ---- == Conditional Independence == If events ''A'' and ''B'' are '''conditionally independent''', then: ''P(A|B,C) = P(A|C)'' ''P(A,B|C) = P(A|C) P(B|C)'' This interrelation is sometimes notated as ''((A⫫B)|C)''. ---- CategoryRicottone |
