1. **State the problem:** We need to find the probability of the union of two events $A$ and $B$ using the formula for not mutually exclusive events. 2. **Formula:** The probability of the union of two events $A$ and $B$ that are not mutually exclusive is given by: $$P(A \cup B) = P(A) + P(B) - P(A \cap B)$$ This formula accounts for the overlap between $A$ and $B$ so that the intersection is not counted twice. 3. **Explanation:** - $P(A)$ is the probability of event $A$ occurring. - $P(B)$ is the probability of event $B$ occurring. - $P(A \cap B)$ is the probability that both $A$ and $B$ occur simultaneously. 4. **Example:** Suppose $P(A) = 0.5$, $P(B) = 0.4$, and $P(A \cap B) = 0.2$. 5. **Calculate:** $$P(A \cup B) = 0.5 + 0.4 - 0.2 = 0.7$$ 6. **Interpretation:** The probability that either event $A$ or event $B$ (or both) occurs is $0.7$. This method ensures we do not double-count the overlap between the two events.