A test for diabetes has a 5% false positive rate, and a 99% true positive rate. This means that 5% of healthy patients wrongly get a positive result, while 99% of diabetes sufferers correctly get a positive result. The prevalence of diabetes in the population being screened is 2%.

a. A patient receives a positive test result. Find the probability that he has diabetes.

b. Are you surprised at the answer you got in part (a)? Explain why it’s so small. Do you think the test is bad?