1. Job Applicants: Job applicants in both the public and private sector are often finding that pre-employment drug testing is a requirement. The Society for Human Resource management found that 71% of larger organizations (25,000+ employees) require drug testing of new job applicants. From the applicant's perspective, one primary concern with drug testing is a \false-positive" result. A \false-positive" is an indication of drug use when the individual has indeed not used drugs. Beyond cost considerations, there are issues of defamation, and wrongful accusations. From the employer's perspective, one primary concern with drug testing is a \false-negative" result. A \false-negative" is where there is no indication of drug use when the individual has indeed used drugs. CyEmployment is one company doing drug testing. To reduce the cost of testing the company uses a cheaper and less accurate test. The following information will be helpful for answering the remaining questions.

• Assume a probability equal to 0.02 that an applicant uses drugs.
• Subset to the group of individuals not using drugs, this test returns a false positive with a probability of 0.09. This is equivalent to saying there is a probability 0.09 that an applicant gets positive test given this individual is not using drugs.
• Subset to the group of individuals who do use drugs, the test also returns a false negative with a probability of 0.02. This is equivalent to saying that there is a probability of 0.02 of a negative test result given an individual is using drugs.

One of CyEmployer's applicants has a very impressive record. Unfortunately, this applicant received a positive test result. What is the probability this applicant actually uses drugs? Think about what the employer knows at this point.

HINT: you may consider creating a contingency table to help you solve this problem.

Use at least 4 decimal places for all parts of your calculations.