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Bayes' Theorem
4. Probability / Bayes' Theorem / Problem 6
Problem 6

A certain disease is present in 2%2\% of a population. A screening test for the disease is positive 85%85\% of the time when the person has the disease and 7%7\% of the time when the person does not have the disease. Let EE be the event "the person has the disease" and FF be the event "the test is positive." What is the probability that a person actually has the disease given that they test positive?