1. **Stating the problem:** We need to find 5 examples of mutually exclusive events where each event has a non-zero probability. 2. **Definition:** Mutually exclusive events are events that cannot happen at the same time. If event A occurs, event B cannot occur simultaneously, so $P(A \cap B) = 0$. 3. **Example 1:** Rolling a fair six-sided die. - Event A: Rolling a 2. - Event B: Rolling a 5. These events cannot happen together because the die shows only one number at a time. 4. **Example 2:** Drawing a single card from a standard deck of 52 cards. - Event A: Drawing a heart. - Event B: Drawing a spade. You cannot draw a card that is both a heart and a spade simultaneously. 5. **Example 3:** Tossing a coin once. - Event A: Getting heads. - Event B: Getting tails. The coin cannot land on both heads and tails at the same time. 6. **Example 4:** Selecting a day of the week. - Event A: Selecting Monday. - Event B: Selecting Friday. A single day cannot be both Monday and Friday. 7. **Example 5:** Choosing a color from a set {red, blue, green}. - Event A: Choosing red. - Event B: Choosing blue. You cannot choose both colors at the same time in a single choice. 8. **Explanation:** In all these examples, the events are mutually exclusive because the occurrence of one event excludes the possibility of the other event occurring simultaneously. 9. **Solution:** Each event has a non-zero probability (e.g., $P(\text{rolling a 2}) = \frac{1}{6}$, $P(\text{drawing a heart}) = \frac{13}{52} = \frac{1}{4}$, $P(\text{heads}) = \frac{1}{2}$, $P(\text{Monday}) = \frac{1}{7}$, $P(\text{red}) = \frac{1}{3}$), and the events cannot happen together, satisfying the mutually exclusive condition.