To identify which pair of events are NOT overlapping when rolling a six-sided die, we need to check if the two events in each pair have any outcomes in common.

Let’s analyze each option:

A) Getting a number greater than 2 and Getting a number less than 5

• Getting a number greater than 2: {3, 4, 5, 6}
• Getting a number less than 5: {1, 2, 3, 4}
• Overlap: {3, 4}

These events do overlap because both 3 and 4 are in common.

B) Getting an odd number and Getting a prime number

• Odd numbers: {1, 3, 5}
• Prime numbers (on a die): {2, 3, 5}
• Overlap: {3, 5}

These events do overlap because 3 and 5 are in common.

C) Getting a number greater than 4 and Getting a number less than 2

• Getting a number greater than 4: {5, 6}
• Getting a number less than 2: {1}
• Overlap: None

These events do not overlap, as there are no numbers common between {5, 6} and {1}.

D) Getting an even number and Getting a prime number

• Even numbers: {2, 4, 6}
• Prime numbers: {2, 3, 5}
• Overlap: {2}

These events do overlap because the number 2 is in common.

---

Conclusion:

The correct answer is: C) Getting a number greater than 4 and Getting a number less than 2

These events do not overlap, as they have no numbers in common.

Would you like more details or have any other questions?

5 Related Questions:

1. What are mutually exclusive events in probability?
2. Can two events overlap if they are independent?
3. How do you calculate the probability of non-overlapping events?
4. What are examples of overlapping events in real-life scenarios?
5. How do you represent overlapping events using Venn diagrams?

Tip:

Non-overlapping events, also called mutually exclusive events, have no common outcomes and their intersection is empty.