Q81 / 160 · AP EAMCET 2007 · Mathematics

If $A$ and $B$ are mutually exclusive events with $P(B) \neq 1$, then $P(A \mid \bar{B})$ is equal to (Here $\bar{B}$ is the complement of the event $B$ )

  • A
    $\frac{1}{P(B)}$
  • B
    $\frac{1}{1-P(B)}$
  • C
    $\frac{P(A)}{P(B)}$
  • Correct answer
    D
    $\frac{P(A)}{1-P(B)}$

Solution

Given, $A$ and $B$ are mutually exclusive events So, $(A \cap B)=\phi$. Now, $\begin{aligned} P(A \mid \bar{B}) & =\frac{P(A \cap \bar{B})}{P(\bar{B})}=\frac{P(A)-P(A \cap B)}{P(\bar{B})} \\ & =\frac{P(A)}{1-P(B)}\end{aligned}$

Hence, the correct answer is option: 'D'.

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