Question

P(A) = 0.4, P(B/A) = 0.9. Then P(A ∩ B) is

• A. 0.36
• B. 0.54
• C. 0.72
• D. 0.84

Hint:

For conditional probability, remember that \( P(B/A) = \frac{P(A \cap B)}{P(A)} \), which allows you to find the intersection of two events when one event is conditional on the other.

Answer 1

The Correct Option is B

We are given: - \( P(A) = 0.4 \) - \( P(B/A) = 0.9 \) We need to find \( P(A \cap B) \), the probability of both events \( A \) and \( B \) occurring. We can use the conditional probability formula: \[ P(B/A) = \frac{P(A \cap B)}{P(A)} \] Rearranging the equation to solve for \( P(A \cap B) \): \[ P(A \cap B) = P(B/A) \times P(A) \] Substituting the given values: \[ P(A \cap B) = 0.9 \times 0.4 = 0.36 \] Thus, the correct answer is 0.36.