Alabar Transportation uses two tests. Random urine testing is applied on a regular basis. If the urine test indicates the presence of an illegal substance, then a blood test is done. Only if the blood test is also positive is action taken.

Both tests occasionally indicate the presence of drugs when there are none. Sometimes they miss drugs. 4% of the time when the employee is using drugs, the urine test does not indicate the presence of any drugs. The blood test makes this error only 1% of the time. 2% of the time when an employee is not using drugs, the urine test indicates that he is. The blood test makes this mistake only 0.8% of the time.

While it may seem that they should use the blood test rather than the urine test, the urine test is quick and costs only $5, whereas the blood test must be sent to a lab, takes 3 days to get results, and costs $200.

We will assume that the urine and blood tests are independent of each other. That means, that the results of the urine test being positive does not affect the accuracy of the blood test. We assume that the accuracy of each test depends only upon whether the person is using drugs.

To explore the effectiveness of the company's testing strategy, we must make an assumption about the prevalence of drug usage. Let us assume that 6% of employees are using drugs.

1. Construct a tree diagram to describe the sequence of events - using drugs, urine test, blood test. Note that the blood test is only done if the urine test is positive. Each branch of the tree should be labeled with what event it represents as well as the probability of this event occurring.

2. Calculate the probabilities of all final outcomes and summarize these in a table like the one below: Positive urine and positive blood test Positive urine test and negative blood test