A medical diagnostic test has a sensitivity (true positive rate) and a specificity (true negative rate). If the disease prevalence is , what is the probability that a person who tests positive actually has the disease (positive predictive value)?
Answer and explanation
Correct answer: A. Approximately
- Step 1: Apply Bayes' theorem: . Step 2. Here . False positive probability is . So . Total positive probability is . Then (). **Answer: Approximately . Why not the others:** confuses sensitivity with positive predictive value; the low base rate () strongly lowers the posterior probability.
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