Complementary Events

An event is the complement of another event if and only if one of the two events must occur but their joint occurrence is impossible, i.e., they are disjoint and exhaustive. More precisely, if

then, in terms of probabilities,

Notes:

• The complement of event A represents the non-occurrence of A.
• As an example, suppose you toss a (regular) coin once and observe what appears on the top face. Then, the complement to the event of getting a `head' is the event of getting a `tail' (and vice versa).
• The Law of Complementation may be used to find the probability of the complement of event A.