A medical test has 95% sensitivity and 90% specificity. If disease prevalence is 1%, the probability that a person with a positive test actually has the disease is approximately: MCQ with Answer and Explanation

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A medical test has 95% sensitivity and 90% specificity. If disease prevalence is 1%, the probability that a person with a positive test actually has the disease is approximately:

A. 15.3%

B. 8.7%

C. 95.0%

D. 50.0%

Answer: Option B

Solution (By JKExamLibrary)

Using Bayes: P(Disease|Positive) = [Sensitivity × Prevalence] / [Sensitivity×Prev + (1-Specificity)×(1-Prev)] = (0.95×0.01) / (0.95×0.01 + 0.10×0.99) = 0.0095 / (0.0095 + 0.099) = 0.0095/0.1085 ≈ 0.0876 ≈ 8.7%. Highlights low positive predictive value when prevalence is low.

This question belongs to: Accountancy and Statistics Statistics

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