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GATE DA 2026 Q57: Probability of disease given a positive test

Question

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)

Try it: numerical answer: type the value

Numerical answer. No negative marking.
Show answer and explanation

Answer: 0.76 to 0.78 (official GATE 2026 final answer key)

Concept used: Bayes' theorem.

First step: P(+)=0.8×0.3+0.1×0.7=0.31P(+) = 0.8 \times 0.3 + 0.1 \times 0.7 = 0.31, and P(D∣+)=0.24/0.31P(D \mid +) = 0.24 / 0.31.

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Source: official GATE 2026 DA question paper and final answer key, organised by IIT Guwahati. Question paper · Answer key

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