5.109 The manufacturer of a low-calorie dairy drink wishes to compare the taste appeal of a new formula

(B) with that of the standard 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 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.