What is the probability that an athlete is a drug user given that the test is positive?

Question

BlackTom AI · Accepted Answer

The prompt asks: 'What is the probability that an athlete is a drug user given that the test is positive?' However, there are no answer options provided, and crucial details are missing to compute a Bayesian probability.

What we would need to calculate P(User | Positive) is:
- The base rate (prior probability) that an athlete is a drug user, P(User).
- The test's sensitivity, i.e., P(Positive | User).
- The test's false positive rate, i.e., P(Positive | Not User) or equivalently specificity, P(Negative | Not User).

With those, we could apply Bayes’ theorem:
P(User | Positive) = [P(Positive | User) * P(User)] / [P(Positive | User) * P(User) + P(Positive | Not User) * P(Not User)].

Since the question provides an answer of 0.679 but does not supply any of the necessary data (base rate, sensitivity, or specificity) and does not present multiple-choice options to evaluate, we cannot verify or derive that numerical result.

If we had typical values for illustration, suppose:
- P(User) = base rate (e.g., 0.05 or 5%),
- Sensitivity = 0.95,
- Specificity = 0.95 (thus P(Positive | Not User) = 0.05).
Then P(User | Positive) would be:
Numerator = 0.95 * 0.05 = 0.0475
Denominator = 0.0475 + (0.05 * 0.95) = 0.0475 + 0.0475 = 0.095
Result ≈ 0.5, i.e., 50%.

This example shows how sensitive the result is to the underlying parameters; changing the base rate or test characteristics can swing the posterior probability up or down significantly.

In summary, with the information given (only the target answer value 0.679 and no options or test parameters), there is insufficient data to perform the calculation or to confirm that 0.679 is correct. To proceed, you would need to provide either:
- The Bayesian inputs (base rate, sensitivity, specificity), or
- The full set of answer options to compare against, or
- Any accompanying context that specifies the test characteristics.

Once any of these are provided, I can compute P(User | Positive) step by step and explain how the result emerges from Bayes’ theorem.

RSM470H1 F LEC0101 In-Class Exercise 10

What is the probability that an athlete is a drug user given that the test is positive?

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RSM470H1 F LEC0101 In-Class Exercise 10

What is the probability that an athlete is a drug user given that the test is positive?

View Explanation

Log in for full answers

Similar Questions

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In a city, 10% of people are vegetarians (V). Among vegetarians, 30% prefer biking as transport (B). Among non-vegetarians (Vc), 15% prefer biking. If a randomly selected person prefers biking, what is the probability that they are vegetarian? (Use Bayes' Theorem)

More Practical Tools for Students Powered by AI Study Helper

Making Your Study Simpler

A factory produces items on two assembly lines, Line 1 (L1) and Line 2 (L2). 60% of items are produced on L1 and 40% on L2. The defect rate for L1 is 5%, and for L2 is 10%. If a randomly selected item is found to be defective (D), what is the probability that it came from Line 1?