A test to detect pollutants is 90% accurate when pollutants are present in a sample and 96% accurate when pollutants are not present. This test is used on a set of samples of which 65% are polluted.
a) For a particular sample, what is the probability that the test says pollutants are present?
b) if the test says that pollutants are not present in a particular sample, what is the probability that is fact there are pollutant in the sample in question?