Question

If A and B are mutually exclusive events with $P\left(B\right)\ne 1$, then $P(A\mid \overline{B})=$

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

Answer 1

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

If A and B are mutually exclusive events then: $P(A\cap B)=0$
$P\left(\frac{A}{\overline{B}}\right)=\frac{P(A\cap \overline{B})}{P\left(\overline{B}\right)}$
Because A and B are mutually exclusive events so $P(A\cap \overline{B})=P\left(A\right)$
$P\left(\frac{A}{\overline{B}}\right)=\frac{P\left(A\right)}{1-P\left(B\right)}$