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 3 glasses in random order, two containing formula A and the other containing formula B. Each judge is asked to state which glass he most enjoyed.Suppose that two formulas are equally attractive.Let X be the number of judges stating a preference for a standard formula (A).

a)Find the probability distribution for a random variable X.

b)What is the probability that at least two of the judges state a preference for a formula A?

c)Find the expected value of a random variable X.

d)Find the variance of a random variable X.