New test for tuberculosis. If the test indicates a person has tuberculosis, the state medical school has discovered that experimentation has shown that the probability of a positive test, given that a person has the test is positive, is 0.06. The probability that the test registers positive, given that the person does not have tuberculosis, is assumed to be 0.06. What is the probability that a person chosen at random will fall into the following categories:
(a) Have tuberculosis and have a positive test
(b) Do not have tuberculosis
(c) Do not have tuberculosis and have a positive test