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# Here the phrase unconditional probability of the

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Unformatted text preview: 2.3 12 +22 +32 +42 +52 +62 6 = 91 6. So Conditional probabilities Let A and B be two events for some probability experiment. The conditional probability of B given A is deﬁned by P (AB ) if P (A) > 0 P ( A) P (B |A) = undeﬁned if P (A) = 0. It is not deﬁned if P (A) = 0, which has the following meaning. If you were to write a computer routine to compute P (B |A) and the inputs are P (AB ) = 0 and P (A) = 0, your routine shouldn’t simply return the value zero. Rather, your routine should generate an error message such as “input error–conditioning on event of probability zero.” Such an error message would help you or others ﬁnd errors in larger computer programs which use the routine. Intuitively, if you know that event A is true for a probability experiment, then you know that the outcome ω of the probability experiment is in A. Conditioned on that, whether B is also true should only depend on the outcomes in B that are also in A, which is the set AB. If B is equal to A, then, given A is true,...
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