To answer the question, we need to evaluate each event to determine which one covers the entire sample space {2, 4, 6, 8, 10}.
1. Event A: The number is greater than 2.
- Sample space: {2, 4, 6, 8, 10}
- Numbers greater than 2: {4, 6, 8, 10}
- This does not include the whole sample space (missing 2).
2. Event B: The number is not divisible by 5.
- Sample space: {2, 4, 6, 8, 10}
- Numbers not divisible by 5: {2, 4, 6, 8}
- This does not include the whole sample space (missing 10).
3. Event C: The number is even and less than 12.
- Sample space: {2, 4, 6, 8, 10}
- Even numbers less than 12: {2, 4, 6, 8, 10}
- This includes the entire sample space.
4. Event D: The number is neither prime nor composite.
- Sample space: {2, 4, 6, 8, 10}
- Non-prime non-composite numbers: This is typically 0 and 1, which don't exist in our set.
- Therefore, this event does not include any numbers from our sample space.
5. Event E: The square root of the number is less than 3.
- Sample space: {2, 4, 6, 8, 10}
- Numbers with square root less than 3: {2} (since sqrt(2) ≈ 1.41 and all larger numbers' square roots are greater than 3)
- This does not include the whole sample space.
From the evaluations, Event C, "The number is even and less than 12," is the only event that covers the entire sample space {2, 4, 6, 8, 10}.
Therefore, the correct answer is:
OC. The number is even and less than 12.
