Question

Question 3 (Multiple Choice Worth 6 points)

(09.01 LC)

Amy is playing a board game and rolls two number cubes. Let A = {the sum of the number cubes is odd}, and let B = {the sum of the number cubes is divisible by 3}. List the outcomes in A ∪ B.
{3, 6, 9, 12}
{1, 3, 5, 7, 9, 11}
{3, 5, 6, 7, 9, 11, 12}
{2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

Answer 1

A = {3, 5, 7, 9, 11}
B = {3, 6, 9, 12}

A ∪ B ={3, 5, 6, 7, 9, 11, 12}

Answer: the third option

Answer 2

Answer with Step-by-step explanation:

Sample space on rolling two number cubes is:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

Sum of the numbers on the cubes lies between 2 and 12

A = {the sum of the number cubes is odd}

={3,5,7,9,11}

B = {the sum of the number cubes is divisible by 3}

={3,6,9,12}

Hence, A ∪ B={3, 5, 6, 7, 9, 11, 12}