Question

If $A$ and $B$ are mutually exclusive events, then $P\left(A\right)>0$ and $P\left(B\right)\ne 1,$ $P\left(\overline{A/B}\right)$ is equal to

• A. $1-P\left(A/B\right)$
• B. $1-p\left(\overline{A}/b\right)$
• C. $\frac{1-P(A\cup B)}{P\left(\overline{B}\right)}$
• D. $\frac{P\left(\overline{A}\right)}{P\left(\overline{B}\right)}.$

Answer 1

The correct option is C $\frac{1-P(A\cup B)}{P\left(\overline{B}\right)}$

$P\left(\overline{A/B}\right)=P\left(\overline{A}/\overline{B}\right)=\frac{P(\overline{A}\cap \overline{B})}{P\left(\overline{B}\right)}=\frac{P\left(\overline{A\cup B}\right)}{P\left(\overline{B}\right)}=\frac{1-P(A\cup B)}{P\left(\overline{B}\right)}$