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:** Tossing a fair coin. Events: A = {Heads}, B = {Tails}. These are mutually exclusive because the coin cannot land both heads and tails at once. Both have $P(A) = 0.5$ and $P(B) = 0.5$. 4. **Example 2:** Rolling a six-sided die. Events: A = {rolling a 2}, B = {rolling a 5}. These are mutually exclusive because the die can only show one number at a time. Both have $P(A) = \frac{1}{6}$ and $P(B) = \frac{1}{6}$. 5. **Example 3:** Drawing a card from a standard deck. Events: A = {drawing a heart}, B = {drawing a club}. These are mutually exclusive because a card cannot be both a heart and a club. Both have $P(A) = \frac{13}{52} = \frac{1}{4}$ and $P(B) = \frac{13}{52} = \frac{1}{4}$. 6. **Example 4:** Selecting a day of the week. Events: A = {Monday}, B = {Friday}. These are mutually exclusive because a day cannot be both Monday and Friday. Both have $P(A) = \frac{1}{7}$ and $P(B) = \frac{1}{7}$. 7. **Example 5:** Choosing a color from a set {Red, Blue, Green}. Events: A = {Red}, B = {Blue}. These are mutually exclusive because the choice cannot be both red and blue simultaneously. Both have $P(A) > 0$ and $P(B) > 0$ depending on the distribution. 8. **Summary:** In all these examples, the events cannot occur together, so they are mutually exclusive, and each event has a positive probability greater than zero.