Bayes' theorem calculator
Apply Bayes' theorem to find the probability of an event given new evidence. Essential for medical testing, spam filters, and decision making.
P(A) — prior
P(B|A) — sensitivity
P(B|not A) — false positive
Bayes' theorem
P(A|B) = P(B|A) × P(A) / P(B)
Where P(B) = P(B|A)×P(A) + P(B|¬A)×P(¬A).
Classic example: medical testing
Disease prevalence: 1%. Test sensitivity (true positive): 95%. False positive rate: 5%.
P(disease | positive test) = (0.95 × 0.01) / (0.95×0.01 + 0.05×0.99) = 0.0095 / 0.059 ≈ 16.1%.
Even with a positive test, there's only a 16% chance of actually having the disease! This is the "base rate fallacy."
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