P(A/B)+P(A非/B非)=1证明AB独立我这样证：原始=P(A/B)+1-P(A/B非)=1则P（A/B）/P(B)=P(A/B非)/P(B非)P（A)=[P(A/B非)P(AB)]P(B)因为我知道要独立就肯定要证P(AB)=P(A)P(B)请问[P(A/B非)P(AB)]怎么推出P(A)的.不是很明白

Answer 1

P(A|B)+P(~A|~B)=1P(A∩B)/P(B) + P(~A∩~B)/P(~B) =1P(A∩B)/P(B) + P(~(AUB)/P(~B) = 1P(A∩B)/P(B) + (1-P(A)-P(B)+P(A∩B))/(1-P(B)) =1P(A∩B)/P(B) + [P(A∩B)-P(A)]/(1-P(B)) =0(1-P(B))P(A∩B) + P(B)[P(A∩...