Home › Previous year questions › GATE 2023 ES › Question 30GATE 2023 ES – Question 30 Mathematics Foundation · Probability and Statistics · 1 mark · Numerical answer
Disease prevalence is .002. A test is positive with probability.98 given disease and .03 given no disease. Find probability of disease given a positive test, to three decimals.
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Show answer and explanation Correct answer: 0.060 to 0.066
Explanation Bayes’ theorem gives $$P(D|+)=\frac{.002(.98)}{.002(.98)+.998(.03)}=\frac{.00196}{.0319}=.0614420.$$ Thus **.061**. Low prevalence allows false positives to outnumber true positives despite high sensitivity.
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