A test is being used to determine whether or not an individual has a disease. It is estimated that, if the individual has the disease, the probability that the test is positive is 0.97. It is also estimated that if the individual does not have the disease, the probability that the test is positive is 0.01. An individual is selected at random from the population and tested. The result is positive.
(a) What is the probability that this individual has the disease if, in the population as a whole, it is estimated that 1 in 10 people have the disease?
(b) What is the probability that this individual has the disease if it is estimated that 1 in 1,000 people in the population have the disease?