Mutually Exclusive Events Calculator

About this calculator

Two events are mutually exclusive (or disjoint) when they cannot both happen at the same time — like rolling a 3 and rolling a 5 on a single die roll. For such events, probability theory's addition rule simplifies to P(A or B) = P(A) + P(B), without the overlap-correcting subtraction term −P(A and B) that's needed for events that can co-occur, since that intersection is always zero.

This distinction is a foundational topic in introductory statistics and probability courses, and it matters in real applications like risk analysis (where two failure modes might be defined as mutually exclusive categories) and game design or gambling odds, where correctly identifying whether outcomes overlap determines whether you simply add probabilities or need the fuller inclusion-exclusion formula.

This calculator takes the probabilities of two mutually exclusive events, computes P(A or B), and also reports the probability that neither event occurs — a quick check for students verifying homework and instructors building example problems.