A rare disease exists with which only 2 in 1000 isaffected. There is a test for the disease that a correct positive result (patientactually has the disease) occurs95%of the time while a false positive result(patient does not have the disease) occurs1%of the time. a) What is the prior distribution of the disease and the posterior distributionof the disease given the positive result?b) Is the test good? Explain that counter-intuitive result.