Four trays of sorted colored tokens and blank row labels. Original AI-generated artwork produced for GreenCalc; not a measured diagram or empirical data display.
Choose the denominator after reading “given”
Consider 100 observations cross-classified by two events. Forty belong to A, fifty belong to B and twenty belong to both. To find P(A | B), restrict attention to the fifty observations in B and ask how many also belong to A. The result is 20/50 = 40%. Reversing the conditioning gives P(B | A) = 20/40 = 50%.
| B | Not B | Total | |
|---|---|---|---|
| A | 20 | 20 | 40 |
| Not A | 30 | 30 | 60 |
| Total | 50 | 50 | 100 |
Convert counts to compatible probability inputs
Enter P(A) = 40%, P(B) = 50% and P(A and B) = 20% in the Conditional Probability Calculator. The joint input uses all 100 observations as its denominator, not the forty or fifty in one marginal group. Every input must refer to the same full population or sample space. Mixing rates from unrelated datasets can create an impossible table.
Use the feasibility bounds as an arithmetic check
A joint probability cannot exceed either marginal probability. It also cannot be less than P(A)+P(B)−1 when that quantity is positive. These bounds keep every cell nonnegative. The calculator enforces them rather than accepting contradictory probabilities and producing a plausible-looking conditional answer.
Distinguish no observations from a zero rate
If P(B) is zero, P(A | B) is undefined by the ordinary ratio. It is not automatically zero. The tool preserves that distinction in its output. To model the table as a binary classifier with an actual and predicted class, use the Confusion Matrix Calculator. Read independence versus mutual exclusivity before inferring a relationship from a conditional rate.
Check the model behind your result
Use the Conditional Probability Calculator for the supported calculation and review its stated assumptions before interpreting the output. Find related tools in the Statistics category, or browse the GreenCalc homepage for other calculation topics.
By GreenCalc Editorial Team · Updated 2026-10-26