1. **State the problem:** Given probabilities $P(A)=0.792$, $P(B)=0.538$, $P(C)=0.783$, and intersections $P(A \cap B)=0.394$, $P(A \cap C)=0.589$, we want to understand these values and possibly find related probabilities. 2. **Recall probability rules:** - The probability of intersection $P(A \cap B)$ represents the chance both events $A$ and $B$ occur. - The probability of union $P(A \cup B)$ can be found using $P(A \cup B) = P(A) + P(B) - P(A \cap B)$. 3. **Calculate $P(A \cup B)$:** $$P(A \cup B) = 0.792 + 0.538 - 0.394 = 0.936$$ 4. **Calculate $P(A \cup C)$:** $$P(A \cup C) = 0.792 + 0.783 - 0.589 = 0.986$$ 5. **Interpretation:** - $P(A \cup B) = 0.936$ means there is a 93.6% chance that either event $A$ or $B$ or both occur. - $P(A \cup C) = 0.986$ means there is a 98.6% chance that either event $A$ or $C$ or both occur. These calculations help understand the combined likelihood of events based on given intersections and individual probabilities.