In a clinic 0.15 of the patients have got the HIV virus. Assume a blood test is carried out on a patient. If the patient has got the virus the test will turn out positive with probability 0.95. If the patient does not have the virus the test will turn out positive with probability 0.02.
If the test is positive what are the probabilities that the patient
(i) has the virus
(ii) does not have the virus? If the test is negative what are the probabilities that the patient
(iii) has the virus
(iv)does not have the virus.