For Exercises 4.14 and 4.15, see pages 180–181; for 4.16 to 4.20, see pages 183–184; for 4.21 to 4.23, see pages 185–186; for 4.24, see page 187; for 4.25 and 4.26, see page 189; and for 4.27 to 4.29, see page 190.
4.28 Failing to detect drug use.
In Example 4.15, we considered how drug tests can indicate illegal drug use when no illegal drugs were actually used. Consider now another type of false test result. Suppose an employee is suspected of having used an illegal drug and is given two tests that operate independently of each other. Test A has probability 0.9 of being positive if the illegal drug has been used. Test B has probability 0.8 of being positive if the illegal drug has been used. What is the probability that neither test is positive if the illegal drug has been used?