设 $A, B$ 为随机事件, 且 $0<P(B)<1$, 下列命题中不成立的是
(A)若 $P(A \mid B)=P(A)$, 则 $P(A \mid \bar{B})=P(A)$.
(B) 若 $P(A \mid B)>P(A)$, 则 $P(\bar{A} \mid \bar{B})>P(\bar{A})$
(C) 若 $P(A \mid B)>P(A \mid \bar{B})$, 则 $P(A \mid B)>P(A)$.
(D) 若 $P(A \mid A \cup B)>P(\bar{A} \mid A \cup B)$, 则 $P(A)>P(B)$.
$P(A \mid A \cup B)=\frac{P(A(A \cup B))}{P(A \bigcup B)}=\frac{P(A)}{P(A)+P(B)-P(A B)}$
$P(\bar{A} \mid A \cup B)=\frac{P(\bar{A}(A \cup B))}{P(A \bigcup B)}=\frac{P(\bar{A} B)}{P(A \bigcup B)}=\frac{P(B)-P(A B)}{P(A)+P(B)-P(A B)}$
因为 $P(A \mid A \cup B)>P(\bar{A} \mid A \cup B)$, 固有 $P(A)>P(B)-P(A B)$, 故正确答案为 D.