6. A contractor doing a construction project needs to decide whether to purchase flood insurance. If the contractor doesn't buy the insurance and flood occurs, the loss is estimated to be $3,000,000. The insurance cost for coverage of $3,000,000 is $300,000. The contractor estimates based on historic record the chance of a flood destroying the project during the season is 10%. The contractor has the option of hiring an expert meteorologist to provide a better forecast. The track record of the meteorologist can be summarized in the following conditional probability table, where Ai is the forecast by the meteorologist and Sj is the actual occurrence. The meteorologist charges $25,000 for the service. P(Aisi) Actual = No Flood Actual = Flood (51) (52) 0.7 0.1 0.25 0.3 0.05 0.6 Forecast Result Forecast No flood Possible flood Very Likely flood A1 A2 Use decision analysis to determine: (a) the best course of actions for the contractor with the help of a decision tree, i.e., first determine whether or not the contractor should use the meteorologist's service, and then given the forecast if the service from meteorologist is used, whether or not to buy insurance (15 points) (b) what is the value of perfect information, if available? (Hint: a perfect forecast will have the following track record) (10 points) P(Cisi) Given State of Nature S2 Test outcomes P1 P2 S1 1.0 0.0 0.0 1.0