The manufacturer of a low-calorie dairy drink wishes to compare the taste appeal of a new formula (formula B) with that of the standard formula (formula A). Each of four judges is given three glasses in random order, two containing formula A and the other containing formula B. Each judge is asked to state which glass he or she most enjoyed. Suppose that the two formulas are equally attractive. Let Y be the number of judges stating a preference for the new formula.
a Find the probability function for Y .
b What is the probability that at least three of the four judges state a preference for the new formula?
c Find the expected value of Y .
d Find the variance of Y.