Bayes’ Theorem Calculator
Combines how likely something was beforehand with how strongly new evidence points to it.
P(H given the evidence)
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Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
P(H given no evidence) —
Overall P(evidence) —
Likelihood ratio —
Reading this —
The formula
P(H | E) = P(E | H) × P(H) ÷ P(E) P(E) = P(E | H)P(H) + P(E | not H)P(not H)
The result depends on how common H is to begin with as well as how good the evidence is.
What to watch out for
Think of 10,000 items of which 1% are faulty. A check flags 90% of the faulty ones and 9% of the good ones. It flags 90 faulty items and 891 good ones, so most flagged items are fine.
Frequently Asked Questions
What is the answer to the faulty items example?
9.174% of flagged items are actually faulty.
What if faults were more common?
With 20% faulty and the same check, 71.43% of flagged items would be faulty.