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Question

10% of the population in a town is HIV^+. A new diagnostic kit for HIV detection is available; this kit correctly identifies HIV^+ individuals 95% of the time, and HIV− individuals 89% of the time. A particular patient is tested using this kit and is found to be positive. The probability that the individual is actually positive is _______

Explanation

Using Bayes theorem, P(HIV|+)=0.95×0.10/(0.95×0.10+0.11×0.90)=0.095/0.194≈0.49. High false positive rate due to low prevalence reduces positive predictive value despite good sensitivity and specificity. Additional evidence from controlled experiments and theoretical models further supports this conclusion in biotechnology literature.

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