Suppose you have data that shows that 12% of athletes test positive for steroids. You also know that 11% of athletes test positive for steroids and actually use steroids. What is the probability that an athlete uses steroids, given that he tests positive?.

the problem ask for the probability that an athlete uses steroid, given that the test is positive if 12% athletes use steroid and the positive that uses steriod is 11% and the answer would be 0.67%, I hope you are satisfied with my asnwer and feel free to ask for more

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virtuematane virtuematane · Answer 2 · 2019-01-04T03:22:04-05:00

Answer:

the probability is: 0.92

Step-by-step explanation:

let the total number of athletes be 'x'. and let 'P' denotes the probability.

let A shows the event that a athlete test positive for steroids.

let B shows the event that athlete use steroids.

as given in the question 12% of the athletes test positive for steroids=0.12 x.

⇒ P(A)=0.12 x

also we know that 11% of the athletes test positive for steroids actually use steroids=0.11 x.

⇒P(A∩B)=0.11 x

Now we are asked to find the probability that an athlete uses steroids, given that he test positive that is we have to find

\(P(B|A)=\frac{P(A\bigcap B)}{P(A)}\)

\(P(B|A)=\frac{0.11 x}{0.12 x}=\frac{11}{12}=0.92\)

Hence, the probability that an athlete uses steroids, given that he tests positive is 0.92.