In a certain test, 5% of patients have a disease. The test is positive for 90% of diseased and 10% of healthy. If a patient tests positive, the probability they have the disease is about: MCQ with Answer and Explanation

In a certain test, 5% of patients have a disease. The test is positive for 90% of diseased and 10% of healthy. If a patient tests positive, the probability they have the disease is about:
A. 0.90
B. 0.10
C. 0.50
D. 0.32
Answer: Option D
Solution (By JKSSB Mock Tests)
P(D)=0.05, P(+|D)=0.9, P(+|D')=0.1. P(D|+) = (0.05×0.9) / (0.05×0.9 + 0.95×0.1) = 0.045/(0.045+0.095)=0.045/0.14≈0.321.

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