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 not divisible by 5.
C) The number is even or less than 12.
D) The number is neither prime nor composite.
E) The square root of the number is less than 3.

Looks like C to me

Note that C covers more than just this set.

To determine which event covers the entire sample space, we need to consider the given set {2, 3, 4, … ,10}.

The sample space consists of all possible outcomes of an experiment. In this case, it is the set of numbers that can be selected at random from the given set.

Let's analyze each event:

A) The event "The number is greater than 2" does not cover the entire sample space because it excludes the numbers 2 and 3.

B) The event "The number is not divisible by 5" does not cover the entire sample space because it excludes the number 5.

C) The event "The number is even or less than 12" covers the entire sample space. All the numbers in the given set are either even or less than 12.

D) The event "The number is neither prime nor composite" does not cover the entire sample space because every number is either prime or composite.

E) The event "The square root of the number is less than 3" covers the entire sample space. When working with real numbers, the square root of any number in the given set will be less than 3.

Therefore, the events C and E cover the entire sample space of this experiment.