You roll two fair dice, a green one and a red one. Required:
a. What is the probability of getting a sum of 8? (Enter your answer as a fraction.)
b. What is the probability of getting a sum of 4?
c. What is the probability of getting a sum of 8 or 4?
d. Are these outcomes mutually exclusive?

Step-by-step explanation:

Given two fair dice are rolled, one green and one red.

To find:

a. Probability of getting a sum of 8.

b. Probability of getting a sum of 4.

c. Probability of getting a sum of 8 or 4.

d. Are these outcomes mutually exclusive?

Solution:

First of all, let us have a look at the output of roll of two dice.

There are a total of 36 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)}

a. Getting a sum equal to 8, we have following outcomes:

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

5 possible outcomes for this event.

Formula for probability of an event E can be observed as:

b. Getting a sum equal to 4, we have following outcomes:

{(1, 3), (2,2), (3, 1)}

3 possible outcomes for this event.

Formula for probability of an event E can be observed as:

c. Probability of getting a sum of 8 or 4?

Following possible outcomes are there:

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

Total 8 possible outcomes:

d. Are these outcomes mutually exclusive?

These events are not mutually exclusive because they contain the similar outcome from both of the dice.

i.e. (4, 4) and (2, 2)