Question

Let \(A\) and \(B\) be two events of a sample space such that \[ P(A)=\frac{1}{2},\qquad P(A\mid B)=\frac{1}{4},\qquad P(B\mid A)=\frac{1}{2}. \] Then, \[ P(\overline{A}\mid\overline{B})=\_\_\_\_\_, \] where \(\overline{A}\) denotes the complement of \(A\).

• A. \( \frac{2}{3} \)
• B. \( \frac{1}{3} \)
• C. \( \frac{3}{4} \)
• D. 0

Hint:

Whenever a conditional probability is asked, always verify that the conditioning event has non-zero probability. If \(P(B)=1\), then \(P(\bar B)=0\), making \(P(\bar A|\bar B)\) undefined.

Answer 1

The Correct Option is D