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 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
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windyyork windyyork · Answer 2 · 2019-06-25T00:50:37-04:00

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%.