1. **Problem:** Two events A and B are mutually exclusive if they cannot happen at the same time. 2. **Example 1:** Tossing a coin. Event A: Getting heads. Event B: Getting tails. 3. **Explanation:** Since a coin cannot show heads and tails simultaneously, these events are mutually exclusive. 4. **Example 2:** Rolling a die. Event A: Getting a 3. Event B: Getting a 5. 5. **Explanation:** A single roll cannot be both 3 and 5, so these events are mutually exclusive. 6. **Example 3:** Drawing a card from a deck. Event A: Drawing a heart. Event B: Drawing a club. 7. **Explanation:** A card cannot be both heart and club at the same time, so these events are mutually exclusive. 8. **Example 4:** Choosing a day. Event A: It is Monday. Event B: It is Tuesday. 9. **Explanation:** A day cannot be both Monday and Tuesday simultaneously, so these events are mutually exclusive. 10. **Example 5:** Selecting a number from 1 to 10. Event A: Number is even. Event B: Number is odd. 11. **Explanation:** A number cannot be both even and odd at the same time, so these events are mutually exclusive. **Summary:** Mutually exclusive events satisfy $P(A \cap B) = 0$, meaning they cannot occur together. **Formula:** $$P(A \cup B) = P(A) + P(B)$$ when A and B are mutually exclusive. This means the probability of either event happening is the sum of their individual probabilities because they cannot happen simultaneously.