select the correct answer. a number is selected at random from the set {2, 4, 6, 8, 10}. which event, by…

select the correct answer. a number is selected at random from the set {2, 4, 6, 8, 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 and less than 12. d. the number is neither prime nor composite. e. the square root of the number is less than 3.

select the correct answer. a number is selected at random from the set {2, 4, 6, 8, 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 and less than 12. d. the number is neither prime nor composite. e. the square root of the number is less than 3.

Answer

Explanation:

Step1: Analyze sample - space elements

The sample space is (S = {2,4,6,8,10}), all of which are even numbers less than 12.

Step2: Analyze option A

The number 2 is not greater than 2, so option A does not cover 2 in the sample - space.

Step3: Analyze option B

The number 10 is divisible by 5, so option B does not cover 10 in the sample - space.

Step4: Analyze option C

All numbers in the set ({2,4,6,8,10}) are even and less than 12. This event covers the entire sample space.

Step5: Analyze option D

All numbers in the set ({2,4,6,8,10}) are either prime (2) or composite ((4,6,8,10)), so this event does not cover any number in the sample - space.

Step6: Analyze option E

(\sqrt{10}\approx3.16>3), so option E does not cover 10 in the sample - space.

Answer:

C. The number is even and less than 12.