A diagnostic test has a probability 0.95 of giving a positive result given (conditioned on) a person is suffering from a certain disease, and a probability 0.10 of giving a (false) positive given...

A diagnostic test has a probability 0.95 of giving a positive result given (conditioned on) a person is suffering from a certain disease, and a probability 0.10 of giving a (false) positive given (conditioned on) a person is non-diseased. It is estimated that 0.5% (convert to 0.005) of the population have the disease. Suppose that the test is now administered to a person about whom we have no relevant information relating to the disease (apart from the fact that he/she comes from this population).

Calculate the following probabilities: (a) that the test result will be positive; (b) that, given a positive result, the person has the disease; (c) that, given a negative result, the person does not have the disease; (d) that the person will be misclassified.