Suppose two dice, one orange and one blue, are rolled. Define the following events: A: The product of the two numbers that show is 12 B: The number on the orange die is strictly larger than the number on the blue die. C: The sum of the numbers is divisible by four. D: The number on the orange die is either 1 or 3

A = {2,6; 6,2; 3,4; 4,3}

B = {6,5; 6,4; 6,3; 6,2; 6,1; 5,4; 5,3; 5,2; 5,1; 4,3; 4,2; 4,1; 3,2; 3,1; 2,1}

C = {1,3; 3,1; 2,2; 3,5; 5,3; 4,4; 6,6}

D = {1,1; 1,2; 1,3; 1,4; 1,5; 1,6; 3,1; 3,2; 3,3; 3,4; 3,5; 3,6}

Step-by-step explanation:

Let the pair (O, B) be the number rolled on the orange and blue dice respectively.

For event A: The product of the two numbers that show is 12, the sample space is:

A = {2,6; 6,2; 3,4; 4,3}

For event B: The number on the orange die is strictly larger than the number on the blue die, the sample space is:

B = {6,5; 6,4; 6,3; 6,2; 6,1; 5,4; 5,3; 5,2; 5,1; 4,3; 4,2; 4,1; 3,2; 3,1; 2,1}

For event C: The sum of the numbers is divisible by four, the sum must be 4, 8 or 12 and the sample space is:

C = {1,3; 3,1; 2,2; 3,5; 5,3; 4,4; 6,6}

For event D: The number on the orange die is either 1 or 3, the sample space is:

D = {1,1; 1,2; 1,3; 1,4; 1,5; 1,6; 3,1; 3,2; 3,3; 3,4; 3,5; 3,6}