Question

概率论基础问题（因为无法输入A的逆事件符号,只好用a来表示,即a=1-A）设A,B满足P(A)=1/2,P(B)=1/3

Answer 1

p(a)=1/2,p(b)=2/3

P(A∣B)=P(AB)/P(B)=3P(AB)

p(a∣b)=p(ab)/p(b)=3p(ab)/2=3p[(1-A)(1-B)]/2

=3P(1-A-B+AB)/2=3[P(1)-P(A)-P(B)+P(AB)]/2

=3[1-1/2-1/3+P(AB)]/2

=1/4+3P(AB)/2

P(A∣B)+ P(a∣b)=3P(AB)+1/4+3P(AB)/2=9P(AB)/2+1/4=1

P(AB)=1/6=P(A)P(B)

即相互独立

P(A∪B) =P(A)+P(B)-P(AB)=1/2+1/3-1/6=2/3