False diagnosis. The fraction of persons in a population who have a certain disease is 0.01 A diagnostic rest is available to test for the disease. But for a healthy person with the chance of being falsely diagnosed as having the disease is 0.05, while for someone with the disease the chance of being falsely diagnosed as healthy is 0.2. suppose the test is performed on a person selected at random from the population.
a) What is the probability that the test shows a positive result (meaning the person is diagnosed as diseased, perhaps correctly, perhaps not)?
b) What is the probability that the person selected at random is one who has the disease but is diagnosed healthy?
c) What is the probability that the person is correctly diagnosed and is healthy?
d) Suppose the test show a positive result. What is probability that the person tested actually has the disease?
e) Do the above probabilities admit a long-run frequency interpretation? Explain.