Question

If \( P(A) = \frac{1}{3} \), \( P(B) = \frac{1}{4} \), and \( P(A \cap B) = \frac{1}{5} \), then \( P(B|A) \) is:

• A. \( \frac{2}{5} \)
• B. \( \frac{3}{5} \)
• C. \( \frac{1}{5} \)
• D. \( \frac{4}{5} \)

Hint:

For conditional probability: \[ P(B|A) = \frac{P(A \cap B)}{P(A)} \] Make sure to simplify the fractions carefully and always check that \( P(A) \neq 0 \).

Answer 1

The Correct Option is B

Step 1: Use the formula for conditional probability: \[ P(B|A) = \frac{P(A \cap B)}{P(A)} \] Step 2: Substitute the given values: \[ P(B|A) = \frac{\frac{1}{5}}{\frac{1}{3}} = \frac{1}{5} \cdot \frac{3}{1} = \frac{3}{5} \] Final Answer: \( \boxed{\frac{3}{5}} \)