Question

概率计算公式,有N多题对于任意两事件A和B,假设已知P(A)=0.5,P(B)=0.6,P(B∣Aˉ)=0.4求P(A+

Answer 1

因为P(A)=0.5,故P(Aˉ)=0.5,

又因为P(B∣Aˉ)=0.4,所以P(BAˉ)=P(B∣Aˉ)*P(Aˉ)=0.4*0.5=0.2.

因此P(AB)=P(BA)=P(B)-P(BAˉ)=0.6-0.2=0.4,

故P(A+B)=P(A)+P(B)-P(AB)=0.5+0.6-0.4=0.7,

P(A-B)=P(A)-P(AB)=0.5-0.4=0.1,

P(A+Bˉ)=P(A)+P(Bˉ)-P(ABˉ)=P(A)-P(ABˉ)+1-P(B)=P(AB)+1-P(B)

=0.4+1-0.6=0.8,

P(A∣Bˉ) =P(ABˉ) /P(Bˉ) =P(A-B)/(1-p(B))=0.1/(1-0.6)=0.25