MHTCET 13 Apr 2026 Shift 2 Paper

Concept:Bayes' theorem is used to find the probability that a person has the disease, given a positive test result.Explanation:Let $D$ be the event that the person has the disease, and let $+$ be the event that the test is positive.Prevalence of the disease: $P(D) = 1\% = 0.01$.Therefore, $P(\bar{D}) = 1 - 0.01 = 0.99$.Sensitivity is the probability of a positive test given the disease: $P(+|D) = 98\% = 0.98$.Specificity is the probability of a negative test given no disease: $P(-|\bar{D}) = 95\% = 0.95$.So the false positive probability is $P(+|\bar{D}) = 1 - 0.95 = 0.05$.We need $P(D|+)$, the probability of disease given a positive test.Using Bayes' theorem: $P(D|+) = \frac{P(D)P(+|D)}{P(D)P(+|D) + P(\bar{D})P(+|\bar{D})}$.Substituting values: $P(D|+) = \frac{0.01 \times 0.98}{(0.01 \times 0.98) + (0.99 \times 0.05)}$.This gives $P(D|+) = \frac{0.0098}{0.0098 + 0.0495} = \frac{0.0098}{0.0593} \approx 0.165$.Hence, $P(D|+) \approx 16.5\%$.Answer:Option C: $16.5\%$