Answer each of the following four questions by choosing an appropriate sample space and assigning probabilities to the various elements of the sample space.
(a) In Leak water township, there are two plumbers. On a particular day three Leak water residents call village plumbers independently of each other. Each resident randomly chooses one of the two plumbers. What is the probability that all three residents will choose the same plumber?
(b) You roll a fair die three times in a row. What is the probability that the second roll will deliver a higher point count than the first roll and the third roll a higher count than the second?
(c) Two players A and B each roll one die. The absolute difference of the outcomes is computed. Player A wins if the difference is 0, 1, or 2; otherwise, player B wins. Is this a fair game?