Let's analyze the events to determine whether they are mutually exclusive for each pair. Mutually exclusive events cannot occur simultaneously.

Pair A: Rolling an odd number vs. Rolling an even number

• Odd numbers on a six-sided die: {1, 3, 5}
• Even numbers on a six-sided die: {2, 4, 6}
• Since no number can be both odd and even, these events are mutually exclusive.

Pair B: Rolling an even number vs. Rolling a prime number

• Even numbers on a six-sided die: {2, 4, 6}
• Prime numbers on a six-sided die: {2, 3, 5}
• The number 2 is both even and prime. Hence, these events are not mutually exclusive.
  Example: Rolling a 2 satisfies both events.

Pair C: Rolling an odd number vs. Rolling a number larger than 4

• Odd numbers on a six-sided die: {1, 3, 5}
• Numbers larger than 4 on a six-sided die: {5, 6}
• The number 5 is both odd and larger than 4. Hence, these events are not mutually exclusive.
  Example: Rolling a 5 satisfies both events.

Let me know if you'd like further clarification or examples!

Related Questions:

1. What are mutually exclusive events, and how do we formally define them in probability?
2. Can you provide more examples of mutually exclusive and non-mutually exclusive events with dice rolls?
3. How would you calculate the probability of two mutually exclusive events occurring?
4. How do you calculate the probability of non-mutually exclusive events using the addition rule?
5. Can mutually exclusive events also be independent? Why or why not?

Tip:

When analyzing events, always check their intersection (shared outcomes). If the intersection is empty, the events are mutually exclusive.