GATE CE 2014 Set 2 — Question 10
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Engineering Mathematics → Probability → Bayes' Theorem
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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 _______
Correct answer
0.48 to 0.49
Solution
Let be the event that a person is HIV positive and be the event that a person is HIV negative.Given:
- Prevalence of HIV:
- Complement:
- Sensitivity (True Positive Rate):
- Specificity (True Negative Rate):
- False Positive Rate:
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