1. 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 3 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 the standard formula (A).
a) List all the elements of the sample space (S)
b) Find the probability distribution for a random variable X
c) What is the probability that at least 2 of the judges state a preference for formula A
d) Find the expected value of a random variable X
e) Find the standard deviation of random variable X
E(X)= Σx P(X)
The Attempt at a Solution
3. I don't really know where to start for this one. I know that each judge has a 2/3 chance of getting formula A and there are 3 judges. I'm confused at how you make the probability distribution for this problem.