Two randomly selected grocery store patrons are each asked to take a blind taste test and to then state which of three diet colas ( marked as A, B, or C) he or she prefers.

a Draw a tree diagram depicting the sample space outcomes for the test results.

b List the sample space outcomes that correspond to each of the following events: ( 1) Both patrons prefer diet cola A. ( 2) The two patrons prefer the same diet cola. ( 3) The two patrons prefer different diet colas. ( 4) Diet cola A is preferred by at least one of the two patrons. ( 5) Neither of the patrons prefers diet cola C.

c Assuming that all sample space outcomes are equally likely, find the probability of each of the events given in part b.