The proportion of people in a given community who have a certaindisease is 0.01. A test is available to diagnose the disease. If aperson has the disease, the probability that the test will producea positive signal is 0.95. If a person does not have the disease,the probability that the test will produce a positive signal is0.02.
a.Given that the test is positive, what is the probability thatthe person has the disease?
b.Given that the test is negative, what is the probability thatthe person does not have the disease?
c.For many medical tests, it is standard procedure to repeat thetest when a positive signal is given. Assume that repeated medicaltests are independent. What is the probability that the person hasthe disease given that two independent tests arepositive?
