A new road is to be built through the Himalayan mountains to the ancient valley of Zarksa. The road will provide access to the valley for tourists, who currently have to travel on mules in a journey that can take up to five days. At some point the road will have to cross the river Yeli and a bridge will be built for this purpose. However, the road builders have yet to decide on the exact location where the road will cross the river. Two options are being considered: Yeli Gorge and Bana. This new road is expected to bring $60 million in revenues to the tourism sector.

If the Yeli Gorge location is chosen it is provisionally estimated that there is a 0.7 probability that the geological conditions will be favorable to the bridge construction and the construction costs will be $40 million. However, should the geological conditions prove unfavorable, the construction costs will soar to $70 million. There is no doubt about the geology at the Bana site and it can be assumed that a bridge built here will be certain to cost $50 million.

a)What is the EMV when no additional information is used? Draw the appropriate decision tree.

Before making the decision on the bridge location, the road builders hear that a specialist in geology will carry out a detailed survey of Yeli Gorge and report on whether the conditions are favorable or unfavorable. However, her methods are not perfectly accurate: When the conditions are good, she has an estimated 80% probability of giving a correct indication. When the conditions are bad, she has an estimated 90% probability of giving a correct indication.

b)Complete the following tables:

Conditional probabilities characterizing expert's prediction, given the geological conditions

Conditions are Favorable

Conditions are not Favorable

Expert says "Favorable"

Expert says "not Favorable"

TOTAL

1.00

1.00

Joint distribution of expert's predictions and geological conditions

Conditions are Favorable

Conditions are not Favorable

TOTAL

Expert says "Favorable"

Expert says "not Favorable"

TOTAL

1.00

Conditional probabilities characterizing geological conditions, given expert's prediction

Conditions are Favorable

Conditions are not Favorable

TOTAL

Expert says "Favorable"

1.00

Expert says "not Favorable"

1.00

c)Compute the EV of II. Draw the appropriate decision tree (only the relevant branch is enough). How much should she ask for maximum as expert's fee?

d)What is the EV of PI? Draw the appropriate decision tree.