Suppose that 16% of the high school athletes in a large school district have taken a banned substance. The drug test used by this district has a false positive rate of 5% and a false negative rate of 10%. If a randomly chosen athlete tests positive, what is the chance that the student actually took a banned substance. Answer the following questions about the district's drug-testing program. What is the probability that a randomly chosen athlete tests positive for banned substances? If two athletes are randomly selected, what's the probability that at least one of them tests positive? What's the probability that a randomly selected athlete did not take a banned substance, given they tested positive? Based on your answer, do you think an athlete who tests positive should be suspended from athletic competition for a year?  Why or why not? What's the probability that a randomly selected athlete took a banned substance given the student tested negative? Explain why it makes sense for th edrug-testing process to be designed so that this probability is less than the one you found in Question 4. The district decides to immediately retest and athlete who tests positive. Assume that the results of an athlete's two tests are independent. Find the probability that a student who gets a positive result on both tests actually took a banned substance (hint: took the banned substance given two positive tests). Based on your answer, do you think that an athlete who tests positive twice should be suspended from athletic competition for a year. Why or why not?

Suppose that 16% of the high school athletes in a large school district have taken a banned substance. The drug test used by this district has a false positive rate of 5% and a false negative rate of 10%. If a randomly chosen athlete tests positive, what is the chance that the student actually took a banned substance. Answer the following questions about the district's drug-testing program.

1. What is the probability that a randomly chosen athlete tests positive for banned substances?
2. If two athletes are randomly selected, what's the probability that at least one of them tests positive?
3. What's the probability that a randomly selected athlete did not take a banned substance, given they tested positive? Based on your answer, do you think an athlete who tests positive should be suspended from athletic competition for a year?  Why or why not?
4. What's the probability that a randomly selected athlete took a banned substance given the student tested negative? Explain why it makes sense for th edrug-testing process to be designed so that this probability is less than the one you found in Question 4.
5. The district decides to immediately retest and athlete who tests positive. Assume that the results of an athlete's two tests are independent. Find the probability that a student who gets a positive result on both tests actually took a banned substance (hint: took the banned substance given two positive tests). Based on your answer, do you think that an athlete who tests positive twice should be suspended from athletic competition for a year. Why or why not?