In a hypothetical population, $2\%$ have a disease. A test returns positive for $90\%$ of t

Question

In a hypothetical population, $2\%$ have a disease. A test returns positive for $90\%$ of those with the disease and negative for $90\%$ of those without it. A person is selected uniformly at random from the population. Find the probability that a person tests positive. It is given that person tests positive. What is the chance they actually have the disease?

Accepted Answer

(i) $0.116$ (ii) $0.155$ (3 s.f.)

Probability - Bayes' Theorem

Probability - Bayes' Theorem

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