Suppose that two balanced dice, a red die, and a green die, are rolled. Let Y denote the value of G - R where G represents the number on the green die and R represents the number on the red die. What are the possible values of the random variable Y?

-5,-4,-3,-2,-1,0,1,2,3,4,5

Step-by-step explanation:

The sample space for the two balanced dice, a red die, and a green die is given below in the pair (G, R)

(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)

For each pair, Y=G-R is presented below:

0 - 1 - 2 - 3 - 4 - 5

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

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

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

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

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

The first column and row is representative of the values which will be obtained throughout the table.

Therefore, the possible values of the random variable Y are:

-5,-4,-3,-2,-1,0,1,2,3,4,5