Management of a company is considering developing a new product. The prior probability of the success of the product in the market is 0.6 and that of the failure is 0.4. If it was successful, the expected profit would be $1,500,000. If unsuccessful, the expected loss would be $1,800,000. A marketing survey can be conducted at a cost of $350,000 to predict whether the product would be successful. Past experience with such surveys indicates that successful products have been predicted to be successful 80 percent of the time, whereas unsuccessful products have been predicted to be unsuccessful 70 percent of the time.

d) Assume now that the market survey is conducted. Find the posterior probabilities of the respective states of nature for each of the two possible predictions from the market survey. (10 marks) e) Find the optimal policy regarding whether to conduct the market survey and whether to develop and market the new product. You should draw a decision tree for this part and write all necessary information on it. (25 marks)