Question

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?.

Answer 1

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 

Answer 2

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.