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

Question

BlackTom AI · Accepted Answer

This question asks for the probability that an athlete is a drug user given that the test result is negative, which is a conditional probability problem that typically requires Bayes' theorem: P(User | Negative) = [P(User) × P(Negative | User)] / P(Negative).

To compute this, we need specific input values:
- P(User): the prior probability (prevalence) of drug use in the athlete population.
- P(Negative | User): the probability of a negative test given that the person is a user, which is 1 minus the test's sensitivity.
- P(Negative): the overall probability of a negative test, which depends on both users and non-users and equals [P(User) × P(Negative | User)] + [P(Non-User) × P(Negative | Non-User)], where P(Negative | Non-User) is the test's specificity.

Because the provided data are incomplete here (no prior prevalence, no sensitivity/specificity, and no negative-test probabilities), a numerical answer like 0.006 cannot be derived definitively from what’s given.

In the absence of those values, here’s how you would proceed if they were supplied:
- Step 1: Identify or estimate P(User) from epidemiological data or assumptions.
- Step 2: Obtain test sensitivity (Se) and specificity (Sp) from validation studies.
- Step 3: Compute P(Negative | User) = 1 − Se.
- Step 4: Compute P(Negative | Non-User) = Sp.
- Step 5: Compute P(Negative) = [P(User) × (1 − Se)] + [(1 − P(User)) × Sp].
- Step 6: Plug into Bayes’ formula to get P(User | Negative).

If you can provide the prevalence (P(User)) and the test’s sensitivity and specificity (or directly P(Negative | User) and P(Negative | Non-User)), I can walk through the calculation and give you the exact numerical result.

RSM470H1 F LEC0101 In-Class Exercise 10

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

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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 negative?

View Explanation

Log in for full answers

Similar Questions

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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?