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?

The possible values of Y are its sample space, and the values are 0, -1, -2, -3, -4, -5, 5, 4, 3, 2 and 1

The sample space of the green die is:

The sample space of the red die is:

When the numbers on both dice are combined, we have the following possible outcomes

(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)

Subtract the second outcomes from the first, to get Y

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

List out the unique numbers:

(0) (-1) (-2) (-3) (-4) (-5) (5) (4) (3) (2) (1)

Hence, the possible values of Y are 0, -1, -2, -3, -4, -5, 5, 4, 3, 2 and 1

Read more about sample space at:

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-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

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