A diagnostic test for a certain disease is said to be 90%
accurate in that, if a person has the disease, the test will detect
it with probability 0.9. Also, if a person does not have the
disease, the test will report that he or she doesn't have it with
probability 0.9. Only 1% of the population has the disease in
question. If a person is chosen at random from the the population
and the diagnostic test reports him to have the disease, what is
the conditional probability that he does, in fact, have the
disease?
Are you surprised by the size of the answer?
Would you call this diagnostic test reliable?
(Please show work) (Given answer shows .4)