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 willbe greater than 0.22, and also a l-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 coherence?

b use appendix f 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.