Consider a town with 10 percent blacks (and the remainder is white). Because blacks are more likely to work the night shifts, 20 percent of all cars driven at night are driven by blacks. One out of every twenty people driving at night is drunk, regardless of race. Persons who are not drunk never swerve their cars, but 10 percent of all drunk drivers, regardless of race, swerve their cars. On a typical night, 5,000 cars are observed by the police force.
(a) What percent of blacks driving at night are driving drunk? What percent of whites driving at night are driving drunk?
(b) Of the 5,000 cars observed, how many are driven by blacks? How many of these cars are driven by a drunk? Of the 5,000 cars observed at night, how many are driven by whites? How many of these cars are driven by a drunk? What percent of nighttime drunk drivers are black?
(c) The police chief believes the drunk-driving problem is mainly due to black drunk drivers. He orders his policemen to pull over all swerving cars and one in every two non-swerving cars that is driven by a black person. The driver of a non-swerving car is then given a breathalyzer test that is 100 percent accurate in diagnosing drunk driving. Under this enforcement scheme, what percent of people arrested for drunk driving will be black?