1. Consider the experiment where two fair six-sided dice are rolled and their face values recorded. a) Find the sample space. b) Given the following vents: A = {(3, 5)} B = a 4 is rolled on the first die C = a 5 is rolled on the second die D = the sum of the dice is 7 E = {(7,4)} Find the following: i. B D and (B D) (A C)c

ii. A D and (A D)c B

2. A coin is tossed four times and the resulting sequence of heads and/or tails is recorded. a) List the elements of events A, B, and C as follows: A: exactly two heads appear B: heads and tails alternate C: first two tosses are heads b) Which events, if any, are mutually exclusive? c) Which events, if any, are subsets of other sets?