Question

P(A) = 0.6,P(B│A) = 0.1,P(B│A的补集 ) = 0.3.求 P(B)

Answer 1

∵P(B│A)=P(AB)/P(A), P(B│A) =0.1 , P(A) =0.6∴ P(AB)= P(B│A) * P(A)=0.1*0.6=0.06 ∵ P ( B│A的补集 ) =0.3,P ( B│A的补集 ) =P ( BA的补集 ) / P(A 的补集 ) ∴P ( BA的补集 ) = P(A 的补集 )* P ( B│A的补集 ) =(1-0.6)*0.3=0.12∴P(B)= P(AB)+ P ( BA的补集 )= 0.06+ 0.12=0.18