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?

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 not a drug user, given that the test is positive?

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?