(10 points) Ideally, the specificity and sensitivity of medical tests should be high (close to 1). However, even with highly specific and sensitive tests, screening a large population for a disease that is rare can produce surprising results.

a. Suppose the sensitivity and specificity of a test for disease are both 0.98. The test is applied to everyone in a population of 100,000 individuals, only 100 of whom have the disease. Organize your results in a table like that in the previous problem by calculating how many individuals with/without the disease you would expect to test positive/negative.

b. Use the table you produced in part (a) to compute the conditional probability that a person who tests positive actually has the disease.