Question

select the correct answer.
a number is selected at random from the set {2, 3, 4, …, 10}. which event, by definition, covers the entire sample space of this experiment?
a. the number is a positive number greater than 2.
b. the number is a positive number that is neither prime nor composite.
c. the number is a positive number that is even or less than 11.
d. the number is a positive number not divisible by 5.

Explanation:

1. First, identify the sample space: $S = \{2, 3, 4, ..., 10\}$, all positive numbers less than 11.
2. Analyze each option:

• Option A: Excludes 2, so it does not cover the full sample space.
• Option B: Only applies to 1, which is not in the sample space.
• Option C: Every number in $S$ is either even OR less than 11 (all numbers in $S$ are less than 11, so this condition is true for every element).
• Option D: Excludes 5 and 10, so it does not cover the full sample space.

Answer:

C. The number is a positive number that is even or less than 11.