Question

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.