You are an executive at Procter and Gamble and are about to introduce a new product. Your boss has asked you to predict the market share (Q, a proportion between 0 and 1) that the new product will capture. You are unsure of Q, and you would like to communicate your uncertainty to the boss. You have made the following assessments: There is a 1-in-10 chance that Q will be greater than 0.22, and also a 1-in-10 chance that Q will be less than 0.08.The value for Q is just as likely to be greater than 0.14 as less than 0.14.
a. What should your subjective probabilities P (0.08, Q, 0.14) and P (0.14, Q, 0.22) be in order to guarantee consistency?
b. Use @RISK to find a beta distribution for Q that closely approximates your subjective beliefs.
c. The boss tells you that if you expect that the market share will be less than 0.15, the product should not be introduced. Write the boss a memo that gives an expected value and also explains how risky you think it would be to introduce the product. Use your beta approximation.