Answer:
Explanation:
To find the probability that an athlete uses steroids given that they test positive, we can use Bayes' theorem.
Let's break down the information given:
- The overall percentage of athletes who test positive for steroids is 12%.
- The percentage of athletes who test positive for steroids and actually use steroids is 11%.
We want to find the probability that an athlete uses steroids given that they test positive. Let's represent this as P(uses steroids | tests positive).
Using Bayes' theorem, we can write:
P(uses steroids | tests positive) = (P(tests positive | uses steroids) * P(uses steroids)) / P(tests positive)
P(tests positive | uses steroids) is the probability that an athlete tests positive given that they use steroids. This information is not provided directly, so we'll make an assumption. Let's assume that the percentage of athletes who use steroids and test positive is 100% (since all athletes who use steroids should test positive).
P(uses steroids) is the overall probability that an athlete uses steroids, which is given as 11%.
P(tests positive) is the overall probability that an athlete tests positive for steroids, which is given as 12%.
Substituting these values into Bayes' theorem:
P(uses steroids | tests positive) = (1 * 0.11) / 0.12
Simplifying the equation:
P(uses steroids | tests positive) = 0.11 / 0.12
Dividing 0.11 by 0.12:
P(uses steroids | tests positive) ≈ 0.92
Therefore, the probability that an athlete uses steroids given that they test positive is approximately 0.92.
The correct answer is E. 0.92.