GATE (GA) Textile 2014 Question Paper Solution | GATE/2014/GA/10

Question 10 (General Aptitude)

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 ____.

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Probabilty(P(A))=0.1 and P(E/A)=0.95
P(B)=0.9 and P(E/B)=1-0.89=0.11
P(A/E),actually HIV +ve=P(A) x P(E/A)/(P(A) x P(E/A)+P(B) x P(E/B))
=0.1 x 0.95/(0.1 x 0.95+0.9 x 0.11)
=0.489 (Ans)

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