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?

Question

22-04-2020
Mathematics

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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?

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Newton9022 Newton9022 · Answer 1 · 2020-04-26T04:57:51+02:00

Answer:

-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

MrRoyal MrRoyal · Answer 2 · 2021-12-09T14:39:45+01:00

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:

[tex]G= \{1,2,3,4,5,6\}[/tex]

The sample space of the red die is:

[tex]R= \{1,2,3,4,5,6\}[/tex]

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