Conditional Probability Calculator
Conditional Probability Calculator
Enter the probability that both events A and B occur together, and the probability of event B occurring on its own. This calculates the conditional probability of A occurring given that B is known to have occurred.
Conditional probability is the mathematical backbone of "given what we now know, how likely is this?" reasoning — medical diagnostics use it to answer "what's the probability of actually having a disease, given a positive test result," insurers use it for risk pricing based on known factors, and it's the foundation Bayes' theorem builds on. The result is only meaningful when P(B) is greater than zero — you can't condition on something that has no chance of happening in the first place.
- Formula: P(A|B) = P(A and B) ÷ P(B) — this is the core definition of conditional probability.
- Only valid when P(B) > 0: you can't condition on an event that has zero probability of happening.
- Common uses: medical test accuracy (probability of disease given a positive test), risk assessment, and any scenario where new information should update your estimate of likelihood.
How is conditional probability different from regular probability?
Regular probability considers the full sample space, while conditional probability narrows the sample space down to only the outcomes where B has already occurred, then asks how often A also occurs within that narrower space.
What if P(A and B) is larger than P(B)?
That combination isn't logically valid, since A-and-B occurring is a subset of B occurring — P(A and B) can never exceed P(B) in a consistent probability model.
Conditional Probability Calculator
Enter the probability that both events A and B occur together, and the probability of event B occurring on its own. This calculates the conditional probability of A occurring given that B is known to have occurred.
Conditional probability is the mathematical backbone of "given what we now know, how likely is this?" reasoning — medical diagnostics use it to answer "what's the probability of actually having a disease, given a positive test result," insurers use it for risk pricing based on known factors, and it's the foundation Bayes' theorem builds on. The result is only meaningful when P(B) is greater than zero — you can't condition on something that has no chance of happening in the first place.
- Formula: P(A|B) = P(A and B) ÷ P(B) — this is the core definition of conditional probability.
- Only valid when P(B) > 0: you can't condition on an event that has zero probability of happening.
- Common uses: medical test accuracy (probability of disease given a positive test), risk assessment, and any scenario where new information should update your estimate of likelihood.
How is conditional probability different from regular probability?
Regular probability considers the full sample space, while conditional probability narrows the sample space down to only the outcomes where B has already occurred, then asks how often A also occurs within that narrower space.
What if P(A and B) is larger than P(B)?
That combination isn't logically valid, since A-and-B occurring is a subset of B occurring — P(A and B) can never exceed P(B) in a consistent probability model.