Conditional Probability Calculator
How a probability changes once you know something else has happened.
P(A given B)
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P(B given A) —
P(A or B) —
Reading this —
The formula
P(A | B) = P(A and B) ÷ P(B)
Knowing B happened shrinks the world to cases where B is true, and asks what share of those also have A.
What to watch out for
P(A given B) and P(B given A) are generally different. Mixing them up is one of the most common errors with probabilities.
Frequently Asked Questions
What is a worked example?
If P(A and B) is 12% and P(B) is 40%, P(A given B) is 30%.
How can I get P(B given A) from P(A given B)?
Using Bayes’ theorem, which needs P(A) and P(B) too.