题目

设事件A，B，C两两独立，则下面选项错误的是（）A.P(AC)=P(A )P(C)-|||-B.P(AC)=P(A )P(C)-|||-C.P(AC)=P(A )P(C)-|||-

设事件A，B，C两两独立，则下面选项错误的是（）

A. $P(\overline{A}C)=P(\overline{A})P(C)$

B. $P\left(ABC\right)=P\left(AB\right)P\left(C\right)$

C. $P(\overline{A}\overline{B})=P(\overline{A})P(\overline{B})$

题目解答

答案

事件A，B，C两两独立，则 $P\left(AB\right)=P\left(A\right)P\left(B\right),P\left(AC\right)=P\left(A\right)P\left(C\right)$ $P\left(BC\right)=P\left(B\right)P\left(C\right),P\left(ABC\right)\ne P\left(A\right)P\left(B\right)P\left(C\right)$ ，则 $P(\overline{A}C)=P\left(C\right)-P\left(AC\right)=P\left(C\right)-P\left(A\right)P\left(C\right)=P(\overline{A})P(C)$ ，选项A正确；

$P(\overline{A}\overline{B})=P(\overline{A\cup B})=1-P\left(A\cup B\right)=1-P\left(A\right)-P\left(B\right)+P\left(AB\right)$ $=1-P\left(A\right)-P\left(B\right)+P\left(A\right)P\left(B\right)=P\left(\overline{A}\right)+P\left(A\right)P\left(B\right)-P\left(B\right)=P(\overline{A})P(\overline{B})$ ，选项C正确，因此选择B。

设事件A，B，C两两独立，则下面选项错误的是（）A.P(AC)=P(A __ )P(C)-|||-__B.P(AC)=P(A __ )P(C)-|||-__C.P(AC)=P(A __ )P(C)-|||-__

题目解答

答案

设事件A，B，C两两独立，则下面选项错误的是（）A.P(AC)=P(A )P(C)-|||-B.P(AC)=P(A )P(C)-|||-C.P(AC)=P(A )P(C)-|||-