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Conditional Probability Calculator
Compute P(A|B) from the joint probability P(A and B) and P(B), and check whether A and B are independent.
P(A and B)
P(B)
P(A) (optional, for the independence check)
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How it works
P(A|B) = P(A ∩ B) ÷ P(B)
Conditioning on B shrinks the sample space to the cases where B occurred, so you divide the joint probability by P(B). If P(A|B) equals P(A), knowing B tells you nothing about A — the events are independent.
Worked example
P(rain and traffic) = 0.12, P(traffic) = 0.4 → P(rain | traffic) = 0.12/0.4 = 0.30.
Frequently asked questions
Is P(A|B) the same as P(B|A)?
No. They share the numerator P(A∩B) but divide by different things. Confusing them is the classic “prosecutor’s fallacy”.
What if I only know P(B|A)?
Use Bayes’ theorem: P(A|B) = P(B|A)·P(A) ÷ P(B).
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