GATE 2026 DA – Question 57
A clinic specializes in testing for a disease D. The result of the test can be either positive or negative.
A study revealed that if a person suffers from the disease D, the test result in that clinic comes out positive 80% of the time, and negative 20% of the time. If a person is not suffering from the disease D, the test comes out positive 10% of the time and negative 90% of the time. It is also known that among the general population, the disease D occurs in 30% of the individuals.
If a person tests positive for D in that clinic, the probability that he/she actually suffers from the disease D is __________ . (*Rounded off to two decimal places*)
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Correct answer: 0.76 to 0.78
Explanation
By Bayes' theorem, $P(D \mid +) = \frac{P(+ \mid D)P(D)}{P(+ \mid D)P(D) + P(+ \mid \neg D)P(\neg D)} = \frac{0.8 \times 0.3}{0.8 \times 0.3 + 0.1 \times 0.7} = \frac{0.24}{0.31} = 0.77$.