A diagnostic test has a probability 0.95 of giving a positive result when applied to a personsuffering from a certain disease, and a probability 0.10 of giving a (false) positive when appliedto a non-sufferer. It is estimated that 0.5 % of the population are sufferers. Suppose that the testis now administered to a person about whom we have no relevant information relating to thedisease (apart from the fact that he/she comes from this population). Calculate the followingprobabilities:(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;(d) that the person will be misclassified.