Conditional Probability Calculator
Calculate P(A|B) using the definition P(A∩B)/P(B) with step-by-step explanation.
About Conditional Probability Calculator
Conditional probability P(A|B) is the probability of event A occurring given that event B has already occurred. It is defined as the ratio of the joint probability P(A∩B) to the marginal probability P(B).
Formula
P(A|B) = P(A ∩ B) / P(B)
- P(A∩B)
- Joint probability of A and B
- P(B)
- Probability of B (must be > 0)
Worked example
With the default values below, Conditional Probability Calculator returns P(A|B) of 0.300000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- P(A ∩ B)accepts 0–1
- 0.12
- P(B)accepts 0–1
- 0.4
Results
- P(A|B)
- 0.300000
Step by step
- 1Values used
- 2Formula applied
- 3P(A|B)= 0.300000
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
When is P(A|B) = P(A)?
When A and B are independent events — knowing B occurred does not change the probability of A.
Is P(A|B) the same as P(B|A)?
No. P(A|B) = P(A∩B)/P(B) while P(B|A) = P(A∩B)/P(A). They are related by Bayes' theorem.