Update a prior probability with new evidence — enter a prior, a likelihood, and a false-positive rate to get the posterior probability.
Your values
Defaults are the classic 1%-prevalence, 95%-accurate test example from our Bayes' theorem article.
Probability tree
P(B) — overall evidence
0.059
Posterior P(A|B)
0.161 (16.1%)
Even with evidence pointing toward A, the posterior probability is 16.1% — much lower than the likelihood alone might suggest, because the low prior means false positives from the much larger unaffected group outweigh true positives.
This is P(B|not A) — the probability of the evidence (like a positive test) occurring even when A (like the condition) is NOT true. For a medical test, this is 1 minus the test's specificity. It's just as important as the true-positive rate (sensitivity) for calculating the posterior correctly.
Why is the posterior often much lower than the likelihood?+−
When the prior (base rate) is low, even a small false-positive rate applied to the much larger group of people who don't have the condition can produce more false positives in absolute terms than true positives from the small group who do. This is the base-rate effect — see the worked example in our Bayes' theorem article.
What if I don’t know the exact prior probability?+−
Use the best available estimate — historical prevalence, a relevant published base rate, or a reasonable informed estimate. The posterior is sensitive to the prior, so if you're unsure, try a few plausible prior values to see how much the conclusion changes (a basic sensitivity check).
Can I chain this calculation for a second piece of evidence?+−
Yes — this is called sequential updating. Take the posterior from this calculation and enter it as the new prior for a second calculation using new likelihood and false-positive-rate values for the next piece of evidence.