Probability

Bayes' Theorem

Compute P(A|B) from P(B|A), P(A), and P(B|A') using Bayes' theorem. See the full step-by-step derivation and the probability tree diagram showing all branches and joint probabilities.

Live Calculator · Step-by-Step · Probability

Inputs

P(A) — Prior probability of A

P(B|A) — Sensitivity (true positive rate)

P(B|A') — False positive rate

Result

Enter values and calculate.

Step-by-Step Work

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Probability Tree