## A drug test for athletes has a 5% false positive rate and a 10% false negative rate. Of the athletes tested, 4% have actually been using the

Question

A drug test for athletes has a 5% false positive rate and a 10% false negative rate. Of the athletes tested, 4% have actually been using the prohibited drug. If a randomly chosen athlete tests positive, what is the probability that the prohibited drug has been used

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2021-09-13T02:43:53+00:00
2021-09-13T02:43:53+00:00 1 Answer
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## Answers ( )

Answer:0.4286 or 42.86%

Step-by-step explanation:The probability that an athlete has used drugs and tests positive is given by the probability that he had been using drugs (4%) multiplied by the probability of a true positive (1 – false negative):

The probability that an athlete has NOT used drugs and tests positive is given by the probability that he had not been using drugs (100% – 4%) multiplied by the probability of a false positive (5%):

Finally, the

probability that the prohibited drug has been used given that an athlete tested positive is:The probability is 0.4286 or 42.86%.