Problem 3: Occasionally a decision is sensitive to the way it is structured. The fol- lowing problem shows that leaving out an important part of the prob- lem can affect the way we view the situation. 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. With- out surgery, your friend will have a shorter and gradually deterio- rating life. Assuming that your friend's objective is to maximize the quality of her life, using PrecisionTree diagram this decision with both an influence diagram and a decision tree. Ondy Decision Tree b. Suppose now that your friend obtains a second opinion. The second physician suggests that there is a third possible outcome: Complica- tions 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. How does this change the decision tree and influence diagram that you created in part a? Draw the decision Only Decision Tree tree. Hints: Part (a) develop the decision tree only. How many options? How many events and their outcomes? Same questions for part (b)