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NDA 2018 Maths · Mathematics · Statistics · hard

In a town, 1% of people have a certain disease. A test is positive for 90% of the people who have the disease and also for 5% of the people who do…

Single correct option

In a town, 1% of people have a certain disease. A test is positive for 90% of the people who have the disease and also for 5% of the people who do not. A person tests positive. The probability that the person has the disease is
  1. A. 910\frac{9}{10}
  2. B. 16\frac{1}{6}
  3. C. 213\frac{2}{13}
  4. D. 958\frac{9}{58}
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Answer: (C) 213\frac{2}{13}

By Bayes' theorem, P(D∣+)=0.01×0.900.01×0.90+0.99×0.05=0.0090.0585=213P(D\mid +)=\frac{0.01\times0.90}{0.01\times0.90+0.99\times0.05}=\frac{0.009}{0.0585}=\frac{2}{13}. The sensitivity 0.9 is not the answer because the disease is rare, so false positives from the large healthy group dominate.
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Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake