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Free Bayes' theorem calculator. Calculate conditional probabilities and update beliefs with step-by-step solutions and statistical methods. Our calculator uses probability principles to determine all statistical relationships from any given events.
Last updated: February 2, 2026
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53.33%
P(A|B) = 0.5333
5.33
Evidence strength
Moderate
Somewhat Confident
10.00%
P(A) = 0.1000
80.00%
P(B|A) = 0.8000
15.00%
P(B) = 0.1500
1. Prior Probability P(A) = 0.1000
2. Likelihood P(B|A) = 0.8000
3. Evidence P(B) = 0.1500
4. Posterior = (0.8000 × 0.1000) / 0.1500
5. Result = 0.5333
Bayes Formula
P(A|B) = P(B|A) × P(A) / P(B)
Bayes Factor
BF = P(B|A) / P(B|¬A)
Evidence Formula
P(B) = P(B|A) × P(A) + P(B|¬A) × P(¬A)
Formula used
P(A|B) = P(B|A) × P(A) / P(B)
Calculates posterior probability from prior, likelihood, and evidence
Uses
Prevalence, Sensitivity, Specificity
Calculates probability of disease given positive test result
Calculates
Positive & Negative Predictive Values
Determines test reliability and clinical significance
Formula used
BF = P(B|A) / P(B|¬A)
Measures relative evidence strength between hypotheses
Features
Prior Updates, Credible Intervals
Updates beliefs based on new evidence
Calculates
Conditional & Joint Probabilities
Handles complex probability relationships
For prior = 0.1, likelihood = 0.8, evidence = 0.15:
Posterior Probability
53.33%
Bayes Factor
5.33
Confidence
Moderate
Our Bayes' theorem calculator uses the fundamental principles of statistical probability to calculate conditional probabilities and update beliefs based on evidence. The calculation applies probability methods and statistical techniques to determine all event relationships.
P(A|B) = P(B|A) × P(A) / P(B)P(A|B) = Posterior ProbabilityP(B|A) = LikelihoodP(A) = Prior ProbabilityP(B) = EvidenceThis formula allows us to update our beliefs about hypothesis A after observing evidence B. It combines our prior knowledge with the likelihood of observing the evidence to produce a posterior probability.
Shows how prior knowledge and evidence combine to form posterior beliefs
Bayes theorem is derived from the definition of conditional probability and the law of total probability. It provides a systematic way to update probabilities when new information becomes available, making it fundamental to statistical inference and decision-making under uncertainty.
Need help with other probability calculations? Check out our probability calculator and binomial distribution calculator.
Get Custom Calculator for Your PlatformResult: Probability of disease given positive test = 48.97%
Despite a positive test, the probability is less than 50% due to low disease prevalence.
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