Answer:
Step-by-step explanation:
The event that, by definition, covers the entire sample space of this experiment is option D: "the number is greater than 1 and less than 99."
Explanation:
In this experiment, we are randomly selecting a number from the set {3, 6, 9, ..., 99}. The sample space of this experiment is the set of all possible outcomes or numbers that can be selected.
Option D, "the number is greater than 1 and less than 99," covers the entire sample space because it includes all the numbers in the given set. The set {3, 6, 9, ..., 99} only contains numbers greater than 1 and less than 99, so option D encompasses all the possible outcomes.
To clarify, let's consider the other options:
- Option A, "the number is neither prime nor composite," does not cover the entire sample space because not all numbers in the given set are neither prime nor composite. For example, 3 is a prime number in the set, while 6 is a composite number.
- Option B, "the square root of a number less than three," does not cover the entire sample space either. The set {3, 6, 9, ..., 99} includes numbers whose square roots are not less than three, such as 9 (sqrt(9) = 3) and 99 (sqrt(99) ≈ 9.95).
- Option C, "the number is divisible by three," also does not cover the entire sample space. While there are numbers in the set that are divisible by three (e.g., 3, 6, 9), there are also numbers that are not divisible by three (e.g., 5, 7, 8).
Therefore, option D, "the number is greater than 1 and less than 99," is the correct answer as it covers the entire sample space of this experiment.
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