设随机事件 $A, B, C$ 满足 $A, C$ 独立, $0 < P(B) < 1,0 < P(C) < 1, P(A \mid C) < P(B \mid C)$, $P(A \mid \bar{C}) < P(B \mid \bar{C})$, 则
A. $P(A)>P(A \mid C B) P(A \mid C)+P(A \mid C \bar{B}) P(\bar{B} \mid C)$.
B. $P(A) < P(A \mid \bar{C} B) P(A \mid \bar{C})+P(A \mid \bar{C} \bar{B}) P(\bar{B} \mid \bar{C})$.
C. $P(A)>P(B \mid C) P(C)+P(B \mid \bar{C}) P(\bar{C})$.
D. $P(A) < P(A \mid B) P(B)+P(A \mid \bar{B}) P(\bar{B})$.