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Problem 1 - Entrance Test

A hospital has a test for a rare disease that affects 0.1% of the population. The test has a 99% accuracy if the person has the disease and a 98% accuracy if the person doesn't. If a person tests positive, what is the probability they actually have the disease?

Correct: B

Using Bayes' theorem: P(Disease|Positive) = [P(Positive|Disease) * P(Disease)] / [P(Positive|Disease) * P(Disease) + P(Positive|No Disease) * P(No Disease)]. Substitute values to get approximately 33%.