CMA Foundation · Fundamentals of Business Mathematics and Statistics · Probability
A diagnostic test for a disease detects it with probability 0.9 in a person who has it, and gives a false positive with probability 0.1 in a person who does not. If 1% of a town's population has the disease, what is the probability that a person testing positive actually has it?
The probability is about 0.083. Positives arise from 0.009 true cases and 0.099 false alarms, total 0.108, so the chance a positive is genuine is 0.009 divided by 0.108, which equals one twelfth.
- A0.9
- B0.5
- C0.09
- D0.083Correct
Explanation
P(positive) = 0.01×0.9 + 0.99×0.1 = 0.009 + 0.099 = 0.108. P(disease | positive) = 0.009/0.108 = 1/12 ≈ 0.083. Option 0.09 ignores the denominator's true value and uses 0.009/0.1.
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