Engineering Board Exam Reviewer · Conditional Probability and Bayes' Theorem · hard
A disease affects 2% of a population. A test detects the disease in 95% of those who have it, but also gives a false positive for 10% of those who do not. If a person tests positive, what is the probability that the person has the disease?
- 0.1624
- 0.95
- 0.1939
- 0.8376
Answer
A. 0.1624
Solution
P(D +)=0.02(0.95)/0.02(0.95)+0.98(0.10)=0.019/0.117 0.1624. Most positives are false positives because the disease is rare.
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