Probability Calculator
Explore common two-event probability relationships using marginal probabilities and an entered intersection.
P(A ∪ B)0.58
P(A | B)0.4
P(B | A)0.3
If independent, P(A∩B)0.12
Enter probabilities between 0 and 1. The intersection must be consistent with the two marginal probabilities for the result to describe a valid probability model.
How this tool works
P(A∪B)=P(A)+P(B)−P(A∩B). Conditional P(A|B)=P(A∩B)/P(B). Independent events would have intersection P(A)P(B).
Example
If P(A)=0.4, P(B)=0.3 and P(A∩B)=0.12, the intersection equals the independence benchmark.
Common questions
What values can probabilities take?
Probabilities should lie between 0 and 1, and the intersection must be consistent with the two marginal probabilities.
Does matching P(A∩B)=P(A)P(B) prove independence?
For two events with the supplied probabilities, that equality is the defining numerical condition for independence.