Suppose that you have three dice, Red, Black, and Yellow. Now one of the dice is selected and rolled.

(a) Find the sample space S for this experiment.

(b) Find the elementary events associated with each of the following events, as well as the probabilities of these events:

(i) the die selected is Yellow and comes up with a number less than 5

(ii) the die selected is Red and comes up with an odd number, or is Black and comes up with an even number.

(c) Show that the color of the die and the number appearing on a roll are independent events. [Hint: Show, by counting elementary events, that the probability of any number and color combination is the product of the number probability and the color probability in this experiment.]]