3. A diagnostic test has a probability 0.95 of giving a positive result when applied to a person suffering from a certain disease, and a probability 0.1 of giving a (false) positive when applied to a
non-sufferer. It is estimated that 0.5% of the population are sufferers. Suppose that the test is now
administered to a person about whom we have no relevant information relating to the disease.
Calculate the following probabilities:
a) That the test result will be positive;
b) that, given a positive result, the person is a sufferer;
c) that, given a negative result, the person is a non-sufferer.