What is the probability that an athlete is not a drug user, given that the test is negative?

Question

BlackTom AI · Accepted Answer

The question asks for P(not drug user | test is negative). To compute this precisely, we need key inputs: the base rate (prevalence) of drug use in the athlete population, the test's sensitivity (P(negative | drug user)), and the test's specificity (P(negative | not drug user)).

Option 1: Without any numeric values for prevalence, sensitivity, or specificity, we cannot determine the posterior probability. Any numerical result would be speculative, because the Bayes formula requires those three components.

Option 2: If we had the prevalence P(D) and the test characteristics, we could apply Bayes’ theorem. Specifically, P(not D | negative) = [P(not D) * P(negative | not D)] / [P(not D) * P(negative | not D) + P(D) * P(negative | D)]. Here, P(negative | not D) equals the specificity, and P(negative | D) equals 1 minus the sensitivity.

Option 3: Misconception to avoid: assuming that a negative test guarantees not being a drug user. A negative result reduces the likelihood but does not necessarily exclude it unless the test is perfectly accurate or the base rate is extremely low. The posterior depends on how common drug use is and how reliable the test is.

Option 4: If one were to attempt a rough intuition, high specificity and low prevalence can push P(not D | negative) toward high values, but this is just intuition. The exact figure requires the exact numbers, not intuition alone.

Option 5: If the given answer 0.994 were to be evaluated, we would need to know the underlying inputs that produced it. Without those inputs, we cannot verify whether 0.994 is correct or under which assumptions it would arise.

In summary, the critical missing pieces are the base rate of drug use in the athlete population and the test’s sensitivity and specificity. With those, you can compute the desired posterior probability using Bayes’ theorem; without them, the probability cannot be determined from the information provided.

RSM470H1 F LEC0101 In-Class Exercise 10

What is the probability that an athlete is not a drug user, given that the test is negative?

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