Answer: P(A | B) * P(B)

## Explanation When two events A and B are **not independent**, the occurrence of one event affects the probability of the other event occurring. In such cases, the joint probability P(A ∩ B) is calculated using the **conditional probability formula**. ### Key Formula: The conditional probability of A given B is defined as: \[ P(A | B) = \frac{P(A \cap B)}{P(B)} \] Rearranging this formula to solve for the joint probability P(A ∩ B): \[ P(A \cap B) = P(A | B) \times P(B) \] ### Why Other Options Are Incorrect: - **Option A (P(A | B)/P(B))**: This is the inverse of the correct formula and would give P(A ∩ B)/[P(B)]², which is incorrect. - **Option C (P(A) * P(B))**: This formula only applies when events A and B are **independent**. For independent events, P(A ∩ B) = P(A) × P(B), but the question specifically states the events are NOT independent. - **Option D (None of the above)**: This is incorrect because Option B provides the correct formula. ### Important Distinction: - **Independent events**: P(A ∩ B) = P(A) × P(B) - **Dependent events**: P(A ∩ B) = P(A | B) × P(B) = P(B | A) × P(A) The question explicitly states "if two events are not independent," so we must use the conditional probability formula for dependent events.

Author: Nikitesh Somanthe