Free · Conditional probability

Bayes’ Rule for Consistent Event Probabilities

Calculate a conditional probability from two event probabilities and the reverse conditional, with checks for a feasible joint distribution.

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If P(A) = 1%, P(B) = 5% and P(B given A) = 80%, then P(A given B) = 16%. The two conditional probabilities are generally different.

P(A given B) = P(B given A) × P(A) ÷ P(B)

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A and B refer to events in the same probability model. Both event probabilities are positive so the two conditional probabilities are defined.
Conditional probabilities lie between 0% and 100%. Their implied intersection cannot exceed either event or be smaller than P(A) + P(B) − 1.
The calculator checks arithmetic consistency, not whether your probability estimates are reliable or applicable to a particular situation.

No. They condition on different events and are connected through the event probabilities.

They may imply an impossible intersection or leave more probability outside A than its complement allows.

Require probabilities at most one, permit zero conditional probabilities, and validate that their implied intersection is feasible.