Question

Suppose that two balanced dice, a red die and a green die, are rolled. Let Y denote opresents the number on the green die and R represents the wo balanced dice are rolled, 36 equally likely 15) Show all work for the following problem. 15) (25 pts) Suppose that two balanced dice, a red die and a green die an the sum G R where G represents the number on the number on the red die. (Hint: When two balanced dice are rolled, 36 outcomes are possible as shown in problem 2).

(1) Can Y=97 Yes or No If yes, please list all the possible outcom Y-9 and find the probability P(Y=9). list all the possible outcomes in the event
(2) What are the possible values of the random variable Y?

Answer 1

1. Yes.

Possible outcome for event Y is:

{(3,6), (4,5), (5,4), (6,3)}

P(Y=9) = 1/9

2. {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}

Explanation:

An image is attached showing the step by step solution

Answer 2

Check the explanation

Explanation:

Y= G+R G

R 1 2 3 4 5 6

1 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

Yes Y can be = 9

((6,3),(5,4),(4,5),(3,6)) are the cases or events.

probability = 4/36=1/9=0.1111

2)

The possible values y are y={1,2,3,4,...,12}

kindly check the attached image below for a more understandable table presentation: