3.2 Conditional Probabilities 3.3 BAYES'FORMULA 3.4 INDEPENDENT EVENTS The multiplication rule If P(A)>0,then P(AB)=P(A)P(BA) If P(AB)>0.then P(ABC)=P(A)P(BA)P(CAB) on>2.If P(A1..An-1)>0,then P(AAn)=P(A)P(A2A)P(AAAn-) Eg.P(A)=0.5.P(B)=0.6.P(BA)=0.8.Find the value of P(AB)and P(A B). 4口t1,13)元，2月00 Xiaohan Yang Chapter 3 Conditional Probability and Independence logo 3.2 Conditional Probabilities 3.3 BAYES’ FORMULA 3.4 INDEPENDENT EVENTS The multiplication rule 1 If P(A) > 0ßthen P(AB) = P(A)P(B|A) 2 If P(AB) > 0, then P(ABC) = P(A)P(B|A)P(C|AB) 3 n ≥ 2ßIf P(A1 · · · An−1) > 0, then P(A1 · · · An) = P(A1)P(A2|A1)· · · P(An|A1 · · · An−1) 4 Eg. P(A) = 0.5, P(B) = 0.6, P(B|A) = 0.8. Find the value of P(AB) and P(A B). Xiaohan Yang Chapter 3 Conditional Probability and Independence