A procedure often used to control the quality of name-brand food products utilizes a panel of five "tasters." Each member of the panel tastes three samples, two of which are from batches of the product known to have the desired taste and the other from the latest batch. Each taster selects the sample that is different from the other two. Assume that the latest batch does have the desired taste, and that there is no communication between the tasters.
a. If the latest batch tastes the same as the other two batches, what is the probability that the taster picks it as the one that is different?
b. What is the probability that exactly one of the tasters picks the latest batch as different?
c. What is the probability that at least one of the tasters picks the latest batch as different?