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home / study / math / statistics and probability / statistics and probability questions and answers / let’s say that we work for the international olympic committee (ioc) as part of their fight ... Your question has been answered Let us know if you got a helpful answer. Rate this answer Question: Let’s say that we work for the International Olympic Committee (IOC) as part of their Fight Again... Let’s say that we work for the International Olympic Committee (IOC) as part of their Fight Against Doping. We have a drug test for a banned performance-enhancing drug (PED) that is 99.3% accurate at identifying the presence of the PED in an athlete’s system. However, it is only 73% accurate at identifying the absence of PED in the athlete’s system. From a scientific study we also have a strong a priori reason to believe that only 3% of Olympic athletes use this particular PED. Use this information, along with Bayes’ Theorem, to answer the following questions:

2. As an employee of the IOC, we don’t want to needlessly ban an athlete from the chance to compete in the Olympics. As a result, we decide to institute a protocol that if an athlete tests positive for the use of the PED we will administer a second test. The second test is less accurate at identifying an athlete that has the PED in their system, at only 81%, but is more accurate at identifying the absence of PED in the athlete’s system, with a probability of 90%. If the athlete tests positive for the PED in both the first and second test, what is the probability that the accused individual uses the banned PED? You may assume the outcome of the second drug test is conditionally independent of the outcome of the first drug test. Hint: Think about Lesson 6, and how to calculate the probability of two independent events both occurring.

Answer 1