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

Question

BlackTom AI · Accepted Answer

We begin by restating what the question asks and what data are needed to compute it.
Question: What is the probability that an athlete is not a drug user, given that the test is positive?
What we need to compute this is Bayes' theorem, which relates the probability of being a non-user given a positive test to the test's characteristics and the base rate:
P(not user | +) = [P(+ | not user) * P(not user)] / [P(+ | not user) * P(not user) + P(+ | user) * P(user)]
Here are the pieces involved:
- P(not user): the prior probability that an athlete is not a drug user (prevalence of non-use).
- P(+ | not user): the false positive rate, i.e., the probability the test is positive given the person is not a user.
- P(user): the prior probability that an athlete is a drug user (1 - P(not user)).
- P(+ | user): the true positive rate, i.e., the probability the test is positive given the person is a user (sensitivity).

Important note about the provided data: the question does not include any values for prevalence, sensitivity, specificity, or even any answer options to compare. The lone answer given (0.321) cannot be verified or derived without these numbers.

Without concrete numbers, here is how you would approach it if they were provided:
- Step 1: Determine P(user) and P(not user) from prevalence data.
- Step 2: Obtain P(+ | user) from the test’s sensitivity.
- Step 3: Obtain P(+ | not user) from the test’s false positive rate, which is 1 minus the specificity.
- Step 4: Plug into Bayes’ formula: compute the numerator and the denominator, then simplify to P(not user | +).

Common pitfalls or misconceptions to watch for:
- Confusing P(+ | user) with P(user | +); the conditional direction matters a lot.
- Forgetting that the prior probabilities (prevalence) are needed; even a highly accurate test can yield a high rate of false positives if the base rate is low.
- Assuming the test’s performance is the same across populations unless specified; prevalence can shift the posterior probability substantially.

If you can provide the values for prevalence (P(user) or P(not user)) and the test’s sensitivity and specificity (or equivalently P(+ | user) and P(+ | not user)), I can compute P(not user | +) step by step and show the numerical result consistent with Bayes’ theorem. As it stands, with no options or data, the 0.321 value cannot be justified from the information given.

RSM470H1 F LEC0101 In-Class Exercise 10

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

查看解析

登录即可查看完整答案

类似问题

Suppose p=0.82. Suppose that the chosen die shows 3. What is the probability that the four-sided die was tossed, i.e., the coin landed on tails?

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

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

What is the probability that a woman who tests positive actually has gestational diabetes? Select the answer that is closest to the actual value.

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?

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)

更多留学生实用工具

希望你的学习变得更简单

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?