GATE BT 2014 • Q10 NAT • 2 Marks

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 - 0.49

Step-by-Step Solution & Explanation

### **Step-by-Step Solution & Mathematical Derivation (GATE BT 2014 Q.10)** **1. Governing Concept & Definition**: - **Topic**: General Aptitude & Bayes' Theorem for Diagnostic Tests - Positive predictive value: $P(\text{HIV}^+ \mid \text{Test}^+) = \frac{P(\text{Test}^+ \mid \text{HIV}^+) P(\text{HIV}^+)}{P(\text{Test}^+)}$ **2. Detailed Step-by-Step Calculation**: - Evaluating sensitivity, specificity, and 10% base prevalence yields: $P \approx 0.485$ **3. Final Answer**: - **Calculated Value**: **0.485** - **Official GATE Accepted Range**: **0.48 to 0.49**

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