Hearing loss A patient with hearing loss is considering whether to have surgery. If she does not have the surgery, her hearing will get no better and no worse. If she does have the surgery, there is an 85 percent chance that her hearing will improve, and a five percent chance that it will deteriorate. If she does not have the surgery, her utility will be zero. If she does have the surgery and her hearing improves, her utility will be ten. If she does have the surgery but her hearing is no better and no worse, her utility will be minus two. If she does have the surgery and her hearing deteriorates, her utility will be minus ten.

(a) Draw a tree representing the decision problem.

(b) Draw a table representing the problem.

(c) What is the expected utility of not having the operation?

(d) What is the expected utility of having the operation?

(e) What should the patient do?