Question 5 (Note that this type of question is very old and not in reference to anything from the past, say, 20 years.) You are getting a test to see if you have a rare disease. You consider yourself to be an average member of the population (in terms of being at-risk for the disease), and on average, 1% of the population has the disease. You take a test that is 90% accurate, meaning if you have the disease it'll return positive 90% of the time and negative 10% of the time, and if you don't have the disease it'll return positive 10% of the time and negative 90% of the time. In other words: P(diseased) = 1 P(healthy) = 0.01 PCpositiveldisease) = 0.9 P(positive|healthy) = 0.1 a. You get a positive test. What is the probability you have the disease? (Hint: Not 90%) You get a negative test. What is the probability you're healthy? (Hint: Not 10%) c. Suppose the value of being healthy is 10 units of utility. The value of having the disease is 2 units of utility. Calculate the expected value (in units of utility) given one receives a positive test. 9