Bayes' Theorem Calculator

Calculate posterior probabilities using Bayes' theorem

Calculate posterior probability using Bayes' theorem with step-by-step explanation

Inputs

P(A) - Prior probability

P(B|A) - Likelihood

P(B|not A) - False positive rate

Calculated P(B) = P(B|A)*P(A) + P(B|not A)*P(not A) = 0.058500

P(A|B) - Posterior Probability

0.153846

15.38%

Step-by-step

P(A|B) = P(B|A) * P(A) / P(B)

P(A|B) = 0.9 * 0.01 / 0.058500

P(A|B) = 0.009000 / 0.058500

P(A|B) = 0.153846

0.01

P(A) Prior

0.9

P(B|A) Likelihood

0.058500

P(B) Evidence

0.153846

P(A|B) Posterior