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

Answer 1

Answer:

a) $P_y = \frac{4}{y} * \frac{1}{3}^y * \frac{2}{3}^{4-y}$

b) 0.033

Step-by-step explanation:

Let Y represents the number of judges preferring a formula.

There are total four judges and each judge can select either A or B

n = 4, p = 1/3

a) The probability function is

$P_y = \frac{4}{y} * \frac{1}{3}^y * \frac{2}{3}^{4-y}$

b)

Substituting the value of y -3 in above equation, we get -

$P_3 = \frac{4}{3} * \frac{1}{3}^3 * \frac{2}{3}^{4-3}\\= \frac{4}{3} * 0.037 * 0.67\\= 0.033$