Exercise 1. Conditional Probability. Suppose that 5% of the employees of a certain company use illegal drugs. The company performs random drug tests that return positive results 98% of the time if the person is a drug user. However, it also has a 4% false positive rate. The results of the test are independent from test to test for a given person. Round your answers to 4 decimals points. Reminder: The false positive rate of a test is defined as the probability that the test returns a positive result while the person was not taking drugs. 1. An employee at the company has a positive test. What is the probability that he uses drugs? 2. Knowing that the first test was positive, what is the probability the second test will be positive? 3. Suppose that the second test is also positive. What is the probability he uses drugs?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Exercise 1. Conditional Probability. Suppose that 5% of the employees of a certain company use illegal
drugs. The company performs random drug tests that return positive results 98% of the time if the person
is a drug user. However, it also has a 4% false positive rate. The results of the test are independent from
test to test for a given person. Round your answers to 4 decimals points.
Reminder: The false positive rate of a test is defined as the probability that the test returns a positive
result while the person was not taking drugs.
1. An employee at the company has a positive test. What is the probability that he uses drugs?
2. Knowing that the first test was positive, what is the probability the second test will be positive?
3. Suppose that the second test is also positive. What is the probability he uses drugs?
Transcribed Image Text:Exercise 1. Conditional Probability. Suppose that 5% of the employees of a certain company use illegal drugs. The company performs random drug tests that return positive results 98% of the time if the person is a drug user. However, it also has a 4% false positive rate. The results of the test are independent from test to test for a given person. Round your answers to 4 decimals points. Reminder: The false positive rate of a test is defined as the probability that the test returns a positive result while the person was not taking drugs. 1. An employee at the company has a positive test. What is the probability that he uses drugs? 2. Knowing that the first test was positive, what is the probability the second test will be positive? 3. Suppose that the second test is also positive. What is the probability he uses drugs?
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