Mutually Exclusive Events

Two events are mutually exclusive when they cannot happen at the same time. Rolling a single die, "getting a 2" and "getting a 5" are mutually exclusive — one roll can't be both at once.

When events can't overlap, the chance that one or the other happens is just their probabilities added together — the OR rule:

P(A \text{ or } B) = P(A) + P(B)

If A and B cannot both happen, add their probabilities for OR: P(A \text{ or } B) = P(A) + P(B).
The probabilities of a complete set of outcomes always sum to 1 — something must happen.
So the chance of an event not happening is P(\text{not } A) = 1 - P(A).

See it on a spinner

Each sector is equally likely. Landing on red and landing on blue are mutually exclusive, so add their chances. Step through the spinner.