Introduction to Risk Analysis, Fall 2001

A carbon monoxide measuring badge is intended to give a positive reading whenever the CO concentration exceeds the public health criterion. The monitor correctly identifies a violation (true positive) in 95% of cases in which a true violation occurs. It also gives false positive readings (i.e., positive reading when there is no violation) in 10% of cases where there is no violation. It is known that the CO problem occurs in 15% of the high-rise buildings in a certain city. If a positive reading is obtained in a certain building, what is the probability that that building has a CO problem? How would the answer change if 20% of the high-rise buildings in the city had CO problems?