Subject: Statistics

Bayes' theorem: probability of disease given a positive test

Update a low base rate with a positive test using Bayes' theorem.

Answer P(A | B) = 0.166667, P(B) = 0.0594

Solution

Given P(A) = 0.01, P(B | A) = 0.99, P(B | A') = 0.05
Complement P(A') = 1 − P(A) = 0.99
Total probability of B P(B) = P(B | A)·P(A) + P(B | A')·P(A') = 0.99·0.01 + 0.05·0.99 = 0.0594
Bayes' theorem P(A | B) = P(B | A)·P(A) / P(B) = (0.99·0.01)/0.0594 = 0.166667

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