Calculate both conditional directions from event marginals and a joint probability, with feasible-table checks and undefined-case handling.
How to use this tool
- Choose the event or model and review the assumptions below.
- Enter the labeled inputs. Probability inputs are percentages from 0 to 100, not decimal fractions.
- Select Calculate and read the labeled outputs.
- Change an input and calculate again; Reset restores the example inputs.
Calculation method
P(A | B) = P(A∩B)/P(B), and P(B | A) = P(A∩B)/P(A).
Assumptions and limits
Joint probability must lie between max(0,P(A)+P(B)−1) and min(P(A),P(B)). Independence is a condition to test, not an automatic assumption. Zero conditioning probabilities yield undefined results.
Worked example
With P(A) = 40%, P(B) = 50% and P(A and B) = 20%, P(A | B) = 20/50 = 40%, while P(B | A) = 20/40 = 50%. The intersection equals 0.4×0.5, so these entered probabilities satisfy independence. The union is 70% and neither event has probability 30%. All three inputs must use the same underlying population.
Worked reading and practical questions
- Read Conditional Probabilities from a Two-Way Count Table
- Independent and Mutually Exclusive Events Are Different
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Frequently asked questions
What does this calculator assume?
Joint probability must lie between max(0,P(A)+P(B)−1) and min(P(A),P(B)). Independence is a condition to test, not an automatic assumption. Zero conditioning probabilities yield undefined results.
How do I enter and update the inputs?
Use the labeled fields, then select Calculate. Percent fields use 0 to 100. After editing, calculate again; Reset restores the example inputs.