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Free conditional probability calculator & Bayes Theorem calculator. Calculate P(A|B) with prior probability, likelihood, and posterior probability. Our calculator uses Bayes' Theorem to update probabilities based on new evidence and calculate conditional probabilities for statistical analysis.
Last updated: February 2, 2026
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Probability of event A (between 0 and 1)
Probability of event B (between 0 and 1)
Probability of B given A (between 0 and 1)
P(A|B) - Posterior Probability
0.2857
Formula:
P(A|B) = P(B|A) × P(A) / P(B)
Calculation Steps:
Interpretation:
Conditional probability is higher than prior probability - event A is more likely given B
Bayes' Theorem:
Formula
P(A|B) = P(B|A) × P(A) / P(B)
Updates probability based on new evidence
Application
Bayesian Inference
Updates beliefs based on new data
Concept
Initial Belief
Starting probability before new evidence
Measure
P(B|A)
Probability of evidence given hypothesis
Application
Diagnostic Testing
Calculate true positive and false positive rates
Analysis
Probability Analysis
Multiple statistical probability measures
Given: P(A) = 0.25, P(B) = 0.35, P(B|A) = 0.40
P(A|B) =
0.2857
(28.57% probability)
Our conditional probability calculator uses Bayes' Theorem to calculate the probability of an event A occurring given that event B has occurred. The calculation combines prior probability, likelihood, and evidence using the formula: P(A|B) = P(B|A) × P(A) / P(B).
Formula:
P(A|B) = P(B|A) × P(A) / P(B)Where:
This fundamental theorem updates probabilities based on new evidence, making it essential for statistical inference, medical diagnosis, and decision-making under uncertainty.
Conditional probability is a fundamental concept in probability theory. It quantifies how the probability of an event changes when we have information about another event. Bayes' Theorem provides a mathematically rigorous way to update probabilities based on evidence, making it the cornerstone of Bayesian inference and statistical reasoning.
Need help with other statistical calculations? Check out our Bayes' theorem calculator and variance calculator.
Get Custom Calculator for Your PlatformProbability of Disease Given Positive Test: 48.9%
Despite a 95% sensitive test, the low prevalence (1%) means only 48.9% of positive tests are true positives. This demonstrates the importance of conditional probability in medical diagnosis.
P(A) = 0.5, P(B) = 0.7, P(B|A) = 0.6
P(A|B) = 0.6 × 0.5 / 0.7 = 0.4286
P(Clouds) = 0.4, P(Rain) = 0.2, P(Clouds|Rain) = 0.9
P(Rain|Clouds) = 0.9 × 0.2 / 0.4 = 0.45
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