Question

I need this fast please

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 greater than 2.
B.
The number is neither prime nor composite.
C.
The number is even or less than 12.
D.
The number is not divisible by 5.

Answer 1

The sample space for the experiment is the set of all possible outcomes. In this case, the set of numbers to select from is {2, 3, 4, 5, 6, 7, 8, 9, 10}.

The event that covers the entire sample space is the one that includes all possible outcomes.

Out of the provided options:

A. "The number is greater than 2" includes {3, 4, 5, 6, 7, 8, 9, 10}, but it does not cover the entire sample space since it excludes the number 2.

B. "The number is neither prime nor composite" is a contradictory statement. All numbers are either prime or composite. This event does not cover the entire sample space.

C. "The number is even or less than 12" includes {2, 3, 4, 5, 6, 7, 8, 9, 10}, which is the same as the sample space, and thus it covers the entire sample space.

D. "The number is not divisible by 5" includes {2, 3, 4, 6, 7, 8, 9}, but it does not include the numbers 5 and 10. Hence, it does not cover the entire sample space.

Therefore, the correct answer is C. "The number is even or less than 12."