Suppose that a medical test has a 92% chance of detecting a disease if the person has it (i.e., 92% sensitivity) and a 94% chance of correctly indicating that the disease is absent if the person really does not have the disease (i.e., 94% specificity). Suppose 10% of the population has the disease.
(a) What is the probability that a randomly chosen person will test positive?
(b) Suppose that a randomly chosen person does test positive. What is the probability that this person really has the disease?