Situations that fit the model
It describes filtered populations, diagnostic subsets, repeated draws, customer segments, and questions containing “given that.” A related application of Conditional Probability is independence.
Math calculator
Conditional Probability Calculator
Calculate P(A|B) from P(A∩B) and P(B). Beside conditional probability, the output shows the operation used to obtain it.
Conditional Probability inputs
Build the expression
Why this relationship works
Conditional probability restricts attention to outcomes inside B. The share also satisfying A is P(A∩B)/P(B).
For this page, conditional probability is interpreted under the stated convention and input order.
Seeing the method in action
If the intersection is 0.18 and P(B)=0.30, then P(A|B)=0.6.
Steps without the calculator
Treat B as the reduced sample space and divide its overlap with A by the total measure of B. Conditional Probability also leads to reverse a condition.
Boundaries and common traps
The conditioning event must have positive probability, and its intersection with A cannot exceed it. P(A|B) usually differs from P(B|A).
Review the sign, scale, and unit of conditional probability after entering intersection probability p(a∩b) and conditioning probability p(b).
A closer look at result behavior
The cleanest input audit is to restate the problem using intersection probability p(a∩b) and conditioning probability p(b). If that sentence sounds wrong, correct the assignment before asking for conditional probability.
How the result responds
Holding the intersection fixed while enlarging B lowers the conditional probability. The pattern also provides a quick estimate of whether a revised result is plausible.
Bayes’ theorem reverses a conditional direction using likelihood, prior, and evidence. The wording of the problem should decide which operation is appropriate.
Recording the answer
The formula and result serve different readers: the formula shows what was done, and the rounded conditional probability communicates scale. Keep both when the work needs review.
A screenshot is unnecessary when the shown formula and the supplied inputs (intersection probability p(a∩b) and conditioning probability p(b)) are saved in plain text. Include the rounding rule if the reported conditional probability is approximate.
Precision and scale in Conditional Probability
Exact arrangement counts from Conditional Probability should not be shortened to a decimal approximation. Probability calculations based on Intersection probability P(A∩B), Conditioning probability P(B) may be rounded for presentation, but their intermediate products and cumulative sums need extra digits so the final tail or complement is not distorted.
For Conditional Probability, keep decimal and percentage forms visibly separate. A result of 0.08 means 8%, not 0.08%, and an input described as 8% normally enters the formula as 0.08. This scale check catches an error much larger than ordinary rounding.
Questions about Conditional Probability
Can P(A|B) exceed P(A)?
Yes.
Why must P(B) be positive?
It is the denominator.
Is P(A|B)=P(B|A)?
Not generally.
What indicates independence?
P(A|B)=P(A).