Problem 38E

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 .

Solution :

Step 1 of 4:

Given four judges is given 3 glasses in random order.

Our goal is:

a). We need to find the probability function for Y.

b). We need to find the probability that at least three of the four judges state a

preference for the new formula.

c). We need to calculate the the expected value of Y.

d). We need to calculate the variance of Y.

a).

Now we have to find the probability function for Y.

Let the number of judges stating a preference for the new formula is Y.

Let Y be a binomial with two random variable n and p.

The formula of the binomial is

,where y=0,1,2,3,4.

Here, Y is binomial with n=4 and p==P(judges chooses formula B).

The probability function for Y is

P(y)=

P(y)=

Hence, P(y)=