Achemist wishes to detect an impurity in a certain compound that she is making. there is a test that detects section 1.5 bayes’ theorem 39 an impurity with probability 0.90; however, this test indicates that an impurity is there when it is not about 5% of the time. the chemist produces compounds with the impurity about 20% of the time; that is, 80% do not have the impurity. a compound is selected at random from the chemist’s output. the test indicates that an impurity is present. what is the conditional probability that the compound actually has an impurity?