Consumer preference. Suppose that half of all computer users prefer the new version of your company’s best-selling software, and half prefer the old version. If you randomly choose three consumers and record their preferences, there are 8 possible outcomes. For example, NNO means the first two consumers prefer the new (N) version and the third consumer prefers the old version (O). All 8 arrangements are equally likely.

(a) Write down all 8 arrangements of preferences of three consumers. What is the probability of any one of these arrangements?

(b) Let X be the number of consumers who prefer the new version of the product. What is the probability that X = 2?

(c) Starting from your work in (a), list the values X can take and the probability for each value.