Question

If two events A and B are such that P(A) > 0 and $P\left(B\right)\ne 1$, then $P\left(\frac{\overline{A}}{\overline{B}}\right)$ is equal to

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

Answer 1

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

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