Bayes' Theorem Calculator
Calculate updated probabilities using Bayes' theorem. Enter the prior probability, the likelihood of evidence given the hypothesis, and the false positive rate to find the posterior probability.
Bayes' theorem updates the probability of a hypothesis based on new evidence.
Formula: P(A|B) = P(B|A) × P(A) / P(B)
Where:
- P(A|B) = posterior probability of A given B
- P(B|A) = likelihood of B given A (sensitivity)
- P(A) = prior probability of A
- P(B) = P(B|A)×P(A) + P(B|not A)×P(not A)
Classic Example: A medical test has 95% sensitivity and 5% false positive rate. If a disease affects 1% of the population, a positive test result means only ~16% chance of actually having the disease. This is the base rate fallacy.