Problem 1 This problem will present the same scenario two different ways the second one will add an additional piece of information. For each scenario, you will construct an influence diagram, as indicated in the problem.

(a) Imagine that a close friend has been diagnosed with heart disease. The physician recommends bypass surgery. The surgery should solve the problem. When asked about the risks, the physician replies that a few individuals die during the operation, but most recover and the surgery is a complete success. Thus, your friend can (most likely) anticipate a longer and healthier life after the surgery. Without surgery, your friend will have a shorter and gradually deteriorating life. Assumingthat your friends objective is to maximize the quality of her life, construct an influence diagram for this scenario.

(b) Suppose now that your friend obtains a second opinion. The second physician suggests that there is a third possible outcome: Complications from surgery can develop which will require long and painful treatment. If this happens, the eventual outcome can be either a full recovery, partial recovery (restricted to a wheelchair until death) or death within a few months. Draw the influence diagram that represents the situation after hearing from both physicians. How does this change the influence diagram that you created in part (a)?