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Olympic athletes undergo a variety of drug tests to ensure the fairness of the competition. Suppose...

Olympic athletes undergo a variety of drug tests to ensure the fairness of the competition. Suppose that 3% of athletes in the 2018 Winter Olympics had taken banned drugs. The drug test has a sensitivity of 98% and a specificity of 95%.

(a) Draw a tree diagram first branching on whether the athlete had taken banned drugs (D or D’) and then on the test result (POS or NEG)?

(b) What is Pr(NEG|D)? Interpret this probability in terms of a medical diagnosis.

(c) What is Pr(D′|POS)? Interpret this probability in terms of a medical diagnosis.

Math   Statistics-And-Probability   
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