Question

It is given that the events \( A \) and \( B \) are such that \[ P(A) = \frac{1}{4}, \quad P(A|B) = \frac{1}{2}, \quad P(B|A) = \frac{2}{3}. \] \text{Then \( P(B) \) is:}

• A. \( \frac{1}{6} \)
• B. \( \frac{1}{3} \)
• C. \( \frac{2}{3} \)
• D. \( \frac{1}{2} \)

Hint:

To find \( P(B) \), use the conditional probability formula \( P(A|B) = \frac{P(A \cap B)}{P(B)} \).

Answer 1

The Correct Option is B

Using the formula \( P(A|B) = \frac{P(A \cap B)}{P(B)} \), we calculate \( P(B) \) as \( \frac{1}{3} \).
Final Answer: \[ \boxed{\frac{1}{3}} \]