Some home builders in recent years are moving towards condominium/townhouse complexes because of the rising cost of detached homes. Spoon Inc. a new builder, must decide if to produce small, medium or large size complexes. The decision is complicated by the state of nature (demand for this type of housing), which can be quite unpredictable. Spoon Inc. consulted a financial analyst who constructed a payoff table (in thousands of dollars) to reflect the alternatives available to the builder:

Complex Size

Demand Large Medium Small

High 1620 1120 850

Moderate 1020 1120 850 Low 800 650 870

The probabilities associated with each state of nature are as follows:

P (high) = P (H) = 0.35; P (moderate) = P (M) = 0.45; P (Low) = P (L) = 0.20

Required:

The builder plans to employ a team of consultants with the following track record to better predict the state of nature.

P(I₁\H) = 0.86 P(I₁\M) = 0.12 P(I₁\L) = 0.02

P(I₂\H) = 0.10 P(I₂\M) = 0.60 P(I₂\L) = 0.30

P(I₃\H) = 0.11 P(I₃\M) = 0.34 P(I₃\L) = 0.55

Where

I₁ market research indicates high demand

I₂ market research indicated medium demand

I₃ market research indicates low demand.

1, Assuming that the consultant indicates a low demand for the product, revise the probabilities (to three decimal places) for high, moderate, and low demand.

2, Does the prediction of a low demand by the consultant change the decision about plant size in part a? Show your calculations.