# Precision Tree

Jim Sellers considers producing a new type of electric razor for men. If the market is favorable, he would get a return of 60000. Since Ron Bush is a good friend of Jim Sellers, Jim is considering the possibility of using Bush Marketing Research Company to gather additional information about the razor market. Bush has suggested that Jim either use a survey, or a pilot study to test the market. The survey is a sophisticated questionnaire administered to a test market, and costs 20000. Ron Bush has proposed Jim to conduct either the survey, or the pilot study before making any decision regarding the production of the new razor. Jim is however not convinced that the contribution of the survey, or that of the pilot study, is worth its cost.

Ron Bush has proposed Jim to conduct either the survey, or the pilot study before making any decision regarding the production of the new razor. Jim is however not convinced that the contribution of the survey, or that of the pilot study, is worth its cost. Jim estimates that the unconditional probability of a successful market is 0.5. Furthermore, the probability of a favorable survey result given a favorable market for razors is 0.7 and the probability of a favorable survey result given an unsuccessful market for razors is 0.2. In addition, the probability of an unfavorable pilot study result given an unfavorable market is 0.9, and the probability of an unfavorable pilot study result given a favorable market for razors is 0.2. Jim wants to use these probability estimates to decide whether to do the survey, or the pilot study, or none.

A) Using PrecisionTree, draw a decision tree to solve Jims problem. Explain how you have calculated all the probabilities that you report on the tree. Define clearly each decision node, event node, decision that you can take, and possible outcome for the random variables.

Let: . FS denote the “favorable survey" outcome . US denote the “unfavorable survey" outcome . FP denote the “favorable pilot study" outcome . UP denote the “unfavorable pilot study" outcome . F denote the “favorable market" scenario . U denote the “unfavorable market" scenario

B) What is the best decision for Jim amongst opting for survey or pilot study or none? Include the decision tree in your analysis/report.

C) Suppose that the cost of the pilot study can be cut down to $15,000. Does it affect Jims best decision?