Question

If \( A \) and \( B \) are independent events and \( P(A) = \frac{2{3} \), \( P(B) = \frac{3}{5} \), then \( P(A' \cap B) = \)}

• A. \( \frac{4}{15} \)
• B. \( \frac{3}{5} \)
• C. \( \frac{2}{5} \)
• D. \( \frac{1}{5} \)

Hint:

For independent events, use \( P(A' \cap B) = P(A') \cdot P(B) \) to find the probability of the intersection.

Answer 1

The Correct Option is D

Step 1: Use the formula for independent events.
For independent events, the probability of \( A' \cap B \) is given by: \[ P(A' \cap B) = P(A') \cdot P(B) \] Since \( P(A') = 1 - P(A) \), we substitute the values of \( P(A) \) and \( P(B) \) to find the answer.
Step 2: Calculation.
Substitute \( P(A) = \frac{2}{3} \) and \( P(B) = \frac{3}{5} \) into the formula to get: \[ P(A' \cap B) = \left(1 - \frac{2}{3}\right) \cdot \frac{3}{5} = \frac{1}{5} \]
Step 3: Conclusion.
The correct answer is (D) \( \frac{1}{5} \).