Understand and apply Bayes' Theorem with ease using our online calculator. Determine the probability of an event based on prior knowledge and new evidence. Ideal for statistics, data analysis, and predictive modeling. Get accurate conditional probabilities quickly for informed decision-making and Bayesian inference.
Formula:
Bayes' Theorem Formula
Bayes' Theorem allows you to update the probability of a hypothesis (A) when new evidence (B) becomes available. The formula is:
P(A|B) = [P(B|A) * P(A)] / P(B)
Where the total probability of evidence P(B) is:
P(B) = P(B|A) * P(A) + P(B|A') * P(A')
- P(A|B): Posterior Probability (the probability of event A occurring given that event B has occurred).
- P(B|A): Likelihood (the probability of event B occurring given that event A has occurred).
- P(A): Prior Probability (the initial probability of event A occurring).
- P(B|A'): Likelihood (the probability of event B occurring given that event A has NOT occurred).
- P(A'): Prior Probability of not A (which is 1 - P(A)).
- P(B): Total Probability of Evidence (the overall probability of event B occurring).