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BayesLab
P(A|B) = P(B|A) · P(A) / P(B).
Bayes' theorem starts with a prior probability (how likely something was before new evidence) and updates it based on how likely that evidence is, given the hypothesis is true versus false.
Even a 99%-accurate test for a rare disease can produce mostly false positives — because the disease is so rare, the small false-positive rate applied to the huge healthy population outnumbers the true positives. This calculator makes that math concrete.
P(A|B)
0.167
P(A|B) = P(B|A)·P(A) / P(B)
What you entered
P(B|A) × P(A)
0.99 × 0.01= 0.0099P(B|¬A) × P(¬A)
0.05 × 0.99= 0.0495Total evidence P(B)
0.0099 + 0.0495= 0.0594Bayes' theorem: P(A|B)
0.0099 ÷ 0.0594= 0.1667Result
P(A|B): 0.167
Starting from a prior of 1%, observing B updates the probability of A to 16.67%.