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 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.