Entrepreneur Vernon Bell would like to determine whether it would be profitable to establish a gardening service in a local suburb. Vernon believes there are four

possible levels of demand for the gardening service:

Very low demand 1% of households would use the service; Vernon would lose $100,000.

Low demand 5% of households would use the service; Vernon would earn $10,000.

Moderate demand 10% of households would use the service; Vernon would earn $25,000.

High demand 29% of households would use the service; Vernon would earn $75,000.

Based on past experiences in other suburbs, Vernon assigns the following probabilities

to the various demand levels:

P(very low demand) = 0.20

P(low demand) = 0.50

P(moderate demand) = 0.20

P(high demand) = 0.10

(a) Set up the decision tree and compute the expected value of offering the

service (2 points).

(b) Compute the expected value with perfect information (1 point).

Vernon decides that prior to a final decision, a survey of the households in this suburb

should be taken to determine demand for the gardening service. If a random sample of

20 households is selected and 3 would use this gardening service: Revise the prior

probabilities in light of this sample information (1 point). (Hint: Use the binomial

distribution to determine the probability of the outcome that occurred given a particular

level of demand.)

(c) What is the revised probability of very low demand? (1 point) (Enter your answer in

the format x.xxxx)

(d) What is the revised probability of high demand? (1 point) (Enter your answer in the

format x.xxxx)

(e) What is the revised expected value of offering the service (1 point)?

(f) What is the revised expected value of perfect information (1 point)?