Consider the situation described in exercise 16.

a. Find the probability of the event that exactly one of the colors that appears face up is red.

b. Find the probability of the event that at least one of the colors that appears face up is red.

Exercise 16

Two faces of a six-sided die are painted red, two are painted blue, and two are painted yellow. The die is rolled three times, and the colors that appear face up on the first, second, and third rolls are recorded.

a. Let BBR denote the outcome where the color appearing face up on the first and second rolls is blue and the color appearing face up on the third roll is red. Because there are as many faces of one color as of any other, the outcomes of this experiment are equally likely. List all 27 possible outcomes.

b. Consider the event that all three rolls produce different colors. One outcome in this event is RBY and another RYB. List all outcomes in the event. What is the probability of the event?

c. Consider the event that two of the colors that appear face up are the same. One outcome in this event is RRB and another is RBR. List all outcomes in the event. What is the probability of the event?