Consider a test which detects if a person has a disease. Let R denote the outcome of the test on a person, D denote whether the person actually has the disease and

be he likelihood that the test gives the correct result. That is, the probability that it

reports that someone has the disease (R= 1) when they actually do (D= 1), is , and

the probability that it reports that someone doesnt have the disease when they dont

is also . Formally: p (R= 1|D= 1) =p(R= 0|D= 0) =.Finally, an -fraction of the population actually has this disease, that is, the prior

probability of a person having this disease is p(D)=.After the results of the first test come back positive, the doctor runs it a second time. Again, it comes back positive. Derive the posterior probability that the person actually has the disease after this second round of testing assuming the two test results are independent and simplify in terms of and . Again, in addition to the general expression, report the values you for = 0.001 and = .95.