Two fair dice are rolled. The first die is red and the second is blue. An experiment consists of observing the numbers that come up on the dice.

a. There are 36 outcomes in the sample space. They are ordered pairs of the form (Red die, Blue die). List the 36 outcomes.

b. Let A be the event that the same number comes up on both dice. List the outcomes in A.

c. Let B be the event that the red die comes up 6.

List the outcomes in B.

d. Let C be the event that one die comes up 6 and the other comes up 1.

List the outcomes in C.

e. Are events A and B mutually exclusive? Explain.

f. Are events A and C mutually exclusive? Explain.