GATE AG 2014 • Q10 NAT • 2 Marks

Section 8: General Aptitude

Quantitative Aptitude

Subtopic: Data Interpretation

Question Statement:

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 _______

Official Answer Key:

0.48 to 0.49

Step-by-Step Solution & Explanation

By Bayes' theorem: P(HIV+|Test+) = P(Test+|HIV+)·P(HIV+) / P(Test+). P(Test+|HIV+) = 0.95, P(HIV+) = 0.10 → numerator = 0.095. P(Test+|HIV−) = 1 − 0.89 = 0.11 (false-positive rate), P(HIV−) = 0.90 → 0.90×0.11 = 0.099. P(Test+) = 0.095 + 0.099 = 0.194. P(HIV+|Test+) = 0.095 / 0.194 = 0.4897, within the accepted range 0.48–0.49. Section 1 Engineering Mathematics

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