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The manufacturer of a drink wishes to compare the taste appeal of the standard formula (formula A) with that of a new formula (formula B). Each of the 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. What is the distribution of Y

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Answer:

P(y) = 4Cy * (2/3)^y * (1/3)^4-y

Step-by-step explanation:

Two distinguishable categories ; A and B ;

Number of cups of formula A given to each judge = 2

Number of cups of formula B given to each judge = 1

Total number of cups = 3

P(formula A) = 2/3

P(formula B) = 1/3

Hence, Probability of each of the two formulas is the same for each judge

Number of judges = 4

Each outcome is independent

y = Number of judges who prefer the new formula

Since, it meets all requirements for a binomial probability distribution :

Hence. The distribution of y ;

4Cy * p(A)^y * p(B)^4-y

P(y) = 4Cy * (2/3)^y * (1/3)^4-y

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