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}