Question

已知P(A拔)=0.3,P(B)=0.4,P(AB拔)=0.5,求条件概率P(B|A+B拔).

Answer 1

P(B)=0.4,可得P(B拔)=0.6

P(AB拔)=0.5

P(A拔)=0.3,可得P(A)=0.7

P(A+B拔)=P(A)+P(B拔)-P(AB拔)=0.7+0.6-0.5=0.8

P(B(A+B拔))=P(AB)=P(A)-P(AB拔)=0.7-0.5=0.2

P(B|A+B拔)=P(B(A+B拔))/P(A+B拔)=1/4