You have a patient with cancer who has a choice between surgery or a chemotherapy. If the patient chooses surgery, she has a 2-percent chance of dying from the operation ( life expectancy = 0 ), a 50-percent of chance being cured ( life expectancy of 15 years), and a 48-percent chance of not being cured ( life expectancy of 2 years). If the patient chooses chemotherapy, she faces 5-percent chance of death (life expectancy of 0), a 65 percent chance of cure ( life expectancy of 15 years), 5 percent chances that her tumor does not responds to chemotherapy (life expectancy of 2 years), and 25 percent of chance that the cancer will be slowed but not cured ( life expectancy of 4 years ).

Create a decision tree and calculate the expected value of each option in terms of life expectancy and conclude that which choice is going to be better.