Sessionville Manufacturing Company plans to introduce a new product known as Quintex. Based on experience and contacts with customers, the vice-president of marketing believes that the demand for Quintex will be between 30,000 and 60,000 units. The following probabilities have been assigned to each possible level of demand:
Demand Probability
30,000 ..................... .10
40,000 ..................... .10
50,000 ..................... .50
60,000 ..................... .30
Before beginning production, the president of the company asked the vice-president of marketing to have the market demand analyzed by an expert system computer program available from a local marketing service company. The program is a market demand analysis model built on the basis of decisions made by several successful experts in the field of market demand analysis. Although the model may overlook some factors unique to the market for Quintex, it captures many important variables and has generally been found to be useful in forecasting product demand. The vice-president complied with the president's request, and the results of the expert system analysis follow:
Demand Probability
30,000 .................... .20
40,000 .................... .50
50,000 .................... .20
60,000 .................... .10
Required:
Using Bayes' theorem, compute the posterior probabilities for the various levels of demand for Quintex, assuming that the demand probabilities generated by the expert system provide new information (that is, assume the expert system probabilities are conditional probabilities).