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Many high schools now have drug testing programs for athletes The main goal of these programs is to reduce the use of banned substances by students who play sports It is not practical to test every athlete for drug use regularly Instead school administrators give drug tests to randomly selected student athletes at unannounced times during the school year Students who test positive face serious consequences including letters to their parents required counseling and suspension from athletic participation Drug tests aren t perfect Sometimes the tests say that athletes took a banned substance when they did not This is known as a false positive Other times drug tests say that athletes are clean when they did take a banned substance This is called a false negative Suppose that 16 of the high school athletes in a large high school have taken a banned substance The drug test used by this high school has a false positive rate of 5 and a false negative rate of 10 The student Mr Brenes was randomly selected and tested positive It your job to defend him at a school board hearing You should do the following 1 Create a sample space for this scenario 2 Calculate appropriate probabilities as well as conditional probabilities Think about what data you would could use to their innocence

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