What Is A Complementary Event?

If we are given a sample space or a universal set S in a probability theory, then any subset of this sample space is known as an event. Let suppose, an event is represented by A and has a probability of occurrence. If we minus this event from the sample space , we get a new set which is known as complementary event of A and represented by A'.

A'= S- A

A and A' are mutually exclusive events because probability of their intersection is equal to zero. These events are also mutually exhaustive because their sum is equal to the sample space i.e. A+A'=S