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

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%.

answer: 15

step-by-step explanation: