Problem 2 (20) - Dr. X has a patient who is very sick. Without further treatment, this patient will die in about 3 months. The only treatment alternative is a risky operation. The patient is expected to live about 1 year if he survives the operation; however, the probability that the patient will not survive the operation is 0.3. a) Draw a decision tree for this simple decision problem. Show all the probabilities and outcome values. b) Let U(x) denote the patient's utility function, where x is the number of months to live. Assuming that U(12) = 1.0 and U(0) = 0, how low can the patient's utility for living 3 months be and still have the operation be preferred