Recall from Exercise 4.3 that two randomly selected customers are each asked to take a blind taste test and then to state which of three diet colas (marked as A, B, or C) he or she prefers. Suppose that cola A's distributor claims that 80 percent of all people prefer cola A and that only 10 percent prefer each of colas B and C.
a. Assuming that the distributor's claim is true and that the two taste test participants make independent cola preference decisions, find the probability of each sample space outcome.
b. Find the probability that neither taste test participant will prefer cola A.
c. If, when the taste test is carried out, neither participant prefers cola A, use the probability you computed in part b to decide whether the distributor's claim seems valid. Explain.