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 probability that an athlete uses steroids, given that he tests positive is 0.92. I am hoping that this answer has satisfied your query and it will be able to help you, and if you would like, feel free to ask another question.

Answer 2

Answer:  Probability that an athlete uses steroids given that he tests positive is 91.6%.

Step-by-step explanation:

Let A be the event that athletes test positive for steroids .

Let B be the event that he actually use steroids.

Since we have given that

Probability that athletes test positive for steroids = P(A) = 12%

Probability that athletes test positive for steroids and actually use steroids = P(A∩B) = 11%

So, we need to find the probability that an athletes use steroids given that he tests positive.

For this we will use "Conditional probability":

$P(B\mid A)=\dfrac{P(A\cap B)}{P(A)}\\\\P(B\mid A)=\dfrac{11}{12}\\\\P(B\mid A)=0.916\\\\P(B\mid A)=0.916\times 100\%\\\\P(B\mid A)=91.6\%$

Hence, Probability that an athlete uses steroids given that he tests positive is 91.6%.