Calculates the probability of event A occurring, given that event B is already known to have occurred.
How it works
The probability of both events happening together is divided by the probability of the condition (event B) alone.
What this does not include
This does not include updating a probability using a reversed conditional — for that, use this site’s Bayes’ theorem calculator instead, which starts from P(B|A) rather than P(A∩B) directly.
How to use this calculator
- Enter P(A and B) and P(B).
A worked example
P(A and B) = 0.2, P(B) = 0.5 → P(A|B) = 0.2 ÷ 0.5 = 0.4.
P(A and B) = 0.1, P(B) = 0.4 → P(A|B) = 0.25.
What the variables mean
| Variable | Meaning |
|---|---|
| P(A and B) | Probability both events happen together |
| P(B) | Probability of the condition (event B) on its own |
Edge cases worth knowing
A P(B) of zero makes the condition itself impossible — there’s no meaningful way to condition on an event that never happens, so the calculator returns no result.
If A and B are independent, P(A|B) equals the plain probability of A — knowing B happened tells you nothing new about A, the defining property of statistical independence.
Frequently asked questions
What does “conditional” mean in this context?
The probability is calculated under the assumption that event B has already happened — it’s a narrower question than the plain (unconditional) probability of A.
Can conditional probability be higher than the plain probability of A?
Yes — if event B makes event A more likely, P(A|B) can be higher than P(A) alone; this is what “informative evidence” looks like in probability terms.
What happens if A and B are independent?
P(A|B) equals P(A) exactly — knowing B happened tells you nothing new about A’s likelihood.
