The eye of Agamoto

Problem Definition

Doctor Stephen Strange is the chief surgeon at the Metropolitan General Hospital in New York. Doctor Strange needs to decide whether to perform surgery or not on a patient with a rare disease. If the patient dies, the hospital must pay a 3M€ compensation, and the cost of the surgery is estimated in 1.5M€. Based on available data, the medical department estimates that the probability of the patient surviving without surgery is 20%, while the probability of the patient surviving with surgery is 75%. Let us use operational research to determine if Doctor Strange should hold the knife:

a. Draw the decision tree to support doctor Strange with this decision problem

b. Solve the decision tree

c. Doctor Strange can use a procedure with a device known as the Eye of Agamoto to get additional information of the result of the surgery, with a cost of 0.5M€. Draw the decision tree incorporating the use of the Eye of Agamoto in the decision problem