1. **Problem:** Two events A and B are mutually exclusive if they cannot happen at the same time. 2. **Definition:** Events A and B are mutually exclusive if $$P(A \cap B) = 0$$. 3. **Example 1:** Tossing a coin. Event A: getting heads, Event B: getting tails. 4. **Explanation:** You cannot get heads and tails simultaneously in one toss, so $$P(A \cap B) = 0$$. 5. **Example 2:** Rolling a die. Event A: rolling a 3, Event B: rolling a 5. 6. **Explanation:** You cannot roll both 3 and 5 at the same time, so $$P(A \cap B) = 0$$. 7. **Example 3:** Drawing a card. Event A: drawing a heart, Event B: drawing a club. 8. **Explanation:** A single card cannot be both heart and club, so $$P(A \cap B) = 0$$. 9. **Example 4:** Selecting a student. Event A: student is male, Event B: student is female. 10. **Explanation:** A student cannot be both male and female simultaneously, so $$P(A \cap B) = 0$$. 11. **Example 5:** Weather forecast. Event A: it rains today, Event B: it is sunny today. 12. **Explanation:** It cannot be raining and sunny at the same time in the same place, so $$P(A \cap B) = 0$$. 13. **Example 6:** Traffic light. Event A: light is red, Event B: light is green. 14. **Explanation:** The light cannot be red and green simultaneously, so $$P(A \cap B) = 0$$. 15. **Example 7:** Exam result. Event A: student passes, Event B: student fails. 16. **Explanation:** A student cannot pass and fail the same exam simultaneously, so $$P(A \cap B) = 0$$. 17. **Example 8:** Choosing a fruit. Event A: fruit is an apple, Event B: fruit is an orange. 18. **Explanation:** A single fruit cannot be both apple and orange, so $$P(A \cap B) = 0$$. 19. **Example 9:** Selecting a day. Event A: day is Monday, Event B: day is Tuesday. 20. **Explanation:** A day cannot be Monday and Tuesday at the same time, so $$P(A \cap B) = 0$$. 21. **Example 10:** Flipping a coin twice. Event A: first flip is heads, Event B: first flip is tails. 22. **Explanation:** The first flip cannot be heads and tails simultaneously, so $$P(A \cap B) = 0$$. **Summary:** Mutually exclusive events cannot occur together, meaning their intersection probability is zero: $$P(A \cap B) = 0$$.