Statistics

Bayes' Theorem Calculator

Update a probability with new evidence.

Calculated Output

P(A | B) 0.1538

P(A | B) (%) 15.385

Formula: P(A|B) = P(B|A)P(A) ÷ [P(B|A)P(A) + P(B|¬A)P(¬A)]

Step-by-Step Breakdown

1. Values used:

2. P(A) prior = 0.01

3. P(B | A) true positive = 0.9

4. P(B | not A) false positive = 0.05

6. P(A | B) = 0.1538

7. P(A | B) = 15.385%

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The math behind it

P(A|B) = P(B|A)·P(A) ÷ [P(B|A)·P(A) + P(B|¬A)·P(¬A)].

1% prior, 90% sensitivity, 5% false positive → ~15.4%.

Surprising result?

With a rare condition, even an accurate test gives many false positives.