Complementary & Mutually Exclusive Events

Complementary events are two outcomes of an event that are the only two possible outcomes.

  • This is like flipping a coin and getting heads or tails. Of course, there are no other options, so these events are complementary.
  • Rolling a die and getting a 1 or 2 are not complementary since there are other outcomes that may happen (3, 4, 5, or 6).
  •  However, rolling a die and getting a 1 or not-a-1 are complementary (you have to roll either a 1 or not-a-1).

Mutually exclusive events, also called disjoint events, are two or more outcomes of an event that cannot occur at the same time.

  • Picking one card from a standard deck and choosing an ace or a king are mutually exclusive events (since you can't do both at the same time).
  • However, choosing a red card or a king are not mutually exclusive (you could choose a red king).

All complementary events are mutually exclusive, but all mutually exclusive events are not necessarily complementary.