1. **State the problem:** We want to find two events from the list that are mutually exclusive when rolling a fair six-sided die once. 2. **Define the events:** - Rolling a factor of 12. Factors of 12 that are possible outcomes on a die are 1, 2, 3, 4, and 6. - Rolling an even number. Even numbers on a die are 2, 4, 6. - Rolling a prime number. Prime numbers on a die are 2, 3, 5. - Rolling a square number. Square numbers on a die are 1 and 4. 3. **Check intersection of pairs:** - Factor of 12 and even number: intersection is {2, 4, 6} (not mutually exclusive) - Factor of 12 and prime number: intersection is {2, 3} (not mutually exclusive) - Factor of 12 and square number: intersection is {1, 4} (not mutually exclusive) - Even number and prime number: intersection is {2} (not mutually exclusive) - Even number and square number: intersection is {4} (not mutually exclusive) - Prime number and square number: intersection is {} (no common element) 4. **Conclusion:** The only pair with no overlap is **Rolling a prime number** and **Rolling a square number**. 5. **Answer:** The two mutually exclusive events are **Rolling a prime number** and **Rolling a square number**.