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):
[tex]P(D\ and\ +) = 0.04*(1-0.10)=0.036[/tex]
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%):
[tex]P(N\ and\ +) = (1-0.04)*0.05=0.048[/tex]
Finally, the probability that the prohibited drug has been used given that an athlete tested positive is:
[tex]P(D|+)=\frac{P(D\ and\ +)}{P(D\ and\ +) \ +\ P(N\ and\ +)} \\P(D|+)=\frac{0.036}{0.036+0.048}=0.4286[/tex]
The probability is 0.4286 or 42.86%.
