第 026 题 / 45

在一个有限样本空间中,假设 $P\left( A\right) = P\left( B\right) = P\left( C\right) = \frac{1}{3}$ ,且 $A$ 与 $B$ 相互独立, $A$ 与 $C$ 互斥,则（ ）
A. $P\left( {A \cup B}\right) = \frac{2}{3}$
B. $P\left( {\bar{C} \mid A}\right) = {2P}\left( {A \mid \bar{C}}\right)$
C. $P\left( {\bar{C} \mid {AB}}\right) = 1$
D. 若 $P\left( {C \mid B}\right) + P\left( {C \mid \bar{B}}\right) = \frac{1}{2}$ ,则 $B$ 与 $C$ 互斥