🎲Conditional Probability Calculator

Calculate P(A|B) from P(A), P(B), and P(A∩B)

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How to Use the Conditional Probability Calculator

The Conditional Probability Calculator computes P(A|B) and P(B|A) from the probabilities of events A and B along with their intersection probability (A∩B). Conditional probability describes the chance that one event happens given that another has already occurred, using the formula P(A|B) = P(A∩B) / P(B). It's widely used in interpreting medical test accuracy, analyzing marketing conversion rates, and solving statistics problems.

Enter all three probability values as percentages, and both conditional probabilities are calculated instantly. Since the intersection probability can never exceed either individual probability — a basic rule of probability — an error message appears if your inputs violate this. Note that P(A|B) and P(B|A) generally differ, since they divide by different denominators (P(B) and P(A) respectively).

Frequently Asked Questions

What is the conditional probability formula?

P(A|B) = P(A∩B) / P(B). It represents the probability that A occurs given that event B has already happened.

Why does it show an error when the intersection is larger than P(A) or P(B)?

The intersection (the probability that A and B both happen) can never exceed the probability of either event alone — this is a basic property of probability.

Are P(A|B) and P(B|A) the same value?

No. Since they have different denominators (P(B) and P(A)), they generally have different values.