Question

Let the S = {0,1,2,3,4,5,6,7,8,9,10} be the sample space of a random experiment. Suppose A is the event that we observe a number less than 3 and B be the event that we observe a number greater than 8. Determine the event that either A occurs or B occurs.

Group of answer choices

{3,4,5,6,7,8}

{0,1,2,3,8,9,10}

empty set

{0,1,2,9,10}

{4,5,6,7}

Answer 1

Let S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be the sample space of a random experiment.

Suppose A is the event that we observe a number less than 3.

A = {0, 1, 2}

Suppose B is the event that we observe a number greater than 8.

B = {9, 10}

The event that either A occurs or B occurs is given by

A B = A + B

A B = {0, 1, 2, 9, 10}

Therefore, the event that either A occurs or B occurs is {0, 1, 2, 9, 10}.