ExamBro
ExamBro
TS EAMCET · Maths · Probability

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 \(B\) )

  1. A \(\frac{1}{P(B)}\)
  2. B \(\frac{1}{1-P(B)}\)
  3. C \(\frac{P(A)}{P(B)}\)
  4. D \(\frac{P(A)}{1-P(B)}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(\frac{P(A)}{1-P(B)}\)

Step-by-step Solution

Detailed explanation

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