L. J. Gant is a builder who has recently acquired a tract of unimproved real estate on which new houses will be built. Gant feels that the local housing market is strong enough to absorb all houses built on the tract by the end of the year, provided the size of the houses meets the needs and preferences of the largest number of home buyers. Four different sizes of houses are being considered-1,600, 2,000, 2,400, and 2,800 square-foot houses. However, for economic and marketing reasons, only one size of house will be built on the tract. Based on past experience, Gant assigned the following subjective probabilities to the size of house most in demand in the local market:
House SizeProbability
1,600 .....................20
2,000 .....................50
2,400 .....................20
2,800 .....................10
Before beginning construction, Gant read in the paper that an electronics firm announced it was considering locating a research laboratory in the community not far from Gant's planned housing site. If the firm locates a research facility in town, it will significantly increase demand for the 2,400- and 2,800-square-foot houses. Gant believes there is a 75% probability that the electronics firm will locate its research facility in town and a 25% probability that it will not. The expected payoff for each alternative is as follows:

Required:
(1) Compute the posterior probabilities for each of the alternatives related to the proposed housing project.
(2) Compute the expected value of each alternative course of action, and make a recommendation to Gant about which course of action to take.

Action: House Size to Build Event (House Size Most in Demand) (in square feet 600 2,000 2,400 2,800 1,600 2,000 2,400 2,800 $200,000 $180,000 $160,000 $140,000 160,000 400,000 360,000 120,000 320,000 600,000 80,000 240,000 480,000 320,000 540,000 800,000