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.