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The senior executives of an oil company are trying to decide whether or not to drill for oil in a particular field in the Gulf of Mexico. It costs the company $1,000,000 to drill in the selected field. Company executives believe that if oil is found in this field its estimated value will be $4,000,000. At present, this oil company believes there is a 45% chance that the selected field actually contains oil. Before drilling, the company can hire a geologist at a cost of $60,000 to prepare a report that contains a recommendation regarding drillin in the selected field. In many similar situations in the past where this geologist has been hired, the geologist has predicted oil on 75% of all fields that have contained oil, and has predicted no oil on 85% of all fields that have not contained oil.
Now consider the case when hiring the geologist is an option. What should the company do?
Draw the decision tree for this problem. Include all of the final payoffs.
Compute the probabilities needed to solve the decision tree? (Hint – there are prior, test and posterior probabilities.)
Solve the tree for the decision strategy that maximizes the average profit for the company. Clearly indicate what action he should take at each decision point.