Bayes Theorem Calculator
Basic Bayes' Theorem
Calculate P(A|B) from P(B|A), P(A), and P(B)
Two-Hypothesis Bayes
Calculate P(A|B) when P(B) is computed from P(B|A) and P(B|not A)
Formula
P(A|B) = P(B|A) × P(A) / P(B) | P(B) = P(B|A)P(A) + P(B|¬A)P(¬A)
Frequently Asked Questions
What is Bayes' Theorem?
Bayes' Theorem calculates the probability of an event based on prior knowledge of related conditions. P(A|B) = P(B|A) × P(A) / P(B). It updates the probability of hypothesis A given new evidence B.
What is a real-world example of Bayes' Theorem?
Medical testing: If a disease affects 1% of people, a test is 99% accurate for positives and 5% false positive rate, then a positive test result means only ~17% chance of actually having the disease. The low prior probability significantly affects the posterior.
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