Two Events, One Picture

Given the chances of event A, event B, and both happening together, this probability calculator reconstructs the full relationship between them: the union, the probability that neither occurs, both conditional probabilities, and whether the two events are independent.

The Union Needs the Overlap

Adding P(A) and P(B) double-counts the region where both occur. Subtracting P(A∩B) once corrects it — that is the inclusion–exclusion principle in its simplest form. When the events cannot co-occur, the overlap is zero and the formula collapses to plain addition.

Dependence Changes the Story

If P(A∩B) differs from P(A) × P(B), the events are dependent: knowing one changes the odds of the other. The conditional probabilities reveal exactly how — P(A|B) tells you the chance of A once B is known, which is the information that drives decision trees and Bayesian reasoning.