Problem $1[30$ points$]$: The senior executives of an oil company are trying to decide whether to drill for oil in a particular field in the Gulf of Mexico. It costs the company $$500,000$ to drill in the selected field. Company executives believe that if oil is found in this field, its estimated value will be $$3,200,000.$ At present, this oil company believes that there is a $30\%$ chance that the selected field contains oil.

a$)$ Suppose that the company can purchase the perfect information on whether the field has oil. Please calculate its EVPI by drawing a complete decision tree manually on a piece of paper or with PrecisionTree in Excel. Show details.

$[10$ points$]$

b$)$ Suppose that the company can hire a geologist to prepare a report that contains a recommendation regarding drilling in the selected field. In many similar situations in the past where this geologist has been hired, the geologist has predicted oil on $80\%$ of all fields that have contained oil and no oil on $75\%$ of all fields that have not contained oil. Please calculate the EVSI of this geologist's recommendation by drawing a complete decision tree manually or with PrecisionTree. Show the probability analysis in a PDF file and the decision tree in a PDF or Excel file.

$[20$ points$]$