Workplace drug testing programs commonly test for various drugs including amphetamines, cocaine, marijuana, and opiates. Suppose that a particular drug test has a false negative rate of 0.10; i.e., if an employee is using drugs, the test will incorrectly test negative with probability 0.10 and correctly indicate positive with probability 0.90.

1. Employees may be tested under the grounds of reasonable suspicion; i.e., if they have exhibited a pattern of unsafe work behavior. Suppose a company decides to test four employees who are correctlysuspected to be using drugs.
   1. Use algebraic methods to find the probability that at least one of the four tested employees will correctly test positive for drug use. State any assumptions required to make the calculation.
   2. Verify your answer to part i. via simulation, using afor() loop to replicate the four tests 100,000 times.
2. Random drug testing is a common strategy for deterring drug use. Suppose a company decides to randomly select four employees for a drug test, and the test has a false negative rate of 0.10. Will the probability that at least one of the four tested employees correctly tests positive for drug use be higher or lower than the probability calculated in part 1)? Explain your answer.