In a certain population, 1 % of individuals have disease D. A screening test A has a sensitivity of 80 % and a false‑positive rate of 5 %. Individuals who test positive on test A are given a second, more specific test B, which has a sensitivity of 90 % and a false‑positive rate of 2 %.
(i) What is the probability that a randomly selected person who tests positive on both tests actually has disease D?
(ii) What is the probability that a person who tests positive on test A but negative on test B has disease D? Give your answers as percentages rounded to two decimal places.

Question

In a certain population, 1 % of individuals have disease D. A screening test A has a sensitivity of 80 % and a false‑positive rate of 5 %. Individuals who test positive on test A are given a second, more specific test B, which has a sensitivity of 90 % and a false‑positive rate of 2 %.  
(i) What is the probability that a randomly selected person who tests positive on both tests actually has disease D?  
(ii) What is the probability that a person who tests positive on test A but negative on test B has disease D? Give your answers as percentages rounded to two decimal places.

Accepted Answer

(i) ≈ 88.00 %; (ii) ≈ 1.62 %

Neco Model Questions Vol1 2025 Mathematics Question 49

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