Mathematics · Probability
Conditional Probability Calculator
Calculate P(A given B) from the intersection and conditioning event.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- 0.2÷0.5=0.4.
Problem → model → reason → result
What problem does this model solve?
Calculate P(A given B) from the intersection and conditioning event.
Why does the model apply?
Conditioning restricts the sample space to outcomes where B occurred.
What assumptions does it make?
Outcomes and selection rules match the stated model; independence, equal likelihood and replacement are assumed only when the problem actually provides them.
Formula
P(A|B)=P(A∩B)/P(B)
Calculation and working
The calculator above substitutes your inputs into the model and leaves the calculation steps visible so the answer can be checked rather than merely accepted.
What does the result mean?
The result answers the stated problem in the units implied by your inputs. Read its sign, size and units together, then compare it with the original values before drawing a conclusion.
Worked example
P(A∩B)=0.2 and P(B)=0.5 gives P(A|B)=0.4.
Common mistake
P(B) must be nonzero and the intersection cannot exceed P(B).
When does this model not apply?
The numerical answer is only as valid as the assumed outcome space and dependence structure.
How to learn with this calculator
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Clear answers
Frequently asked questions
What does the Conditional probability do?
Calculate P(A given B) from the intersection and conditioning event.
How does the Conditional probability work?
The calculator applies P(A|B)=P(A∩B)/P(B). Conditioning restricts the sample space to outcomes where B occurred.
What can I learn from the Conditional probability?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed 2026-07-14. Calculations tested 2026-07-14.