Complementary Events
Two events A and B are complementary if1. A and B are mutually exclusive.
2. A and B are mutually exhaustive.
The first of the these dictates that A and B cannot both happen. You can flip a coin and get heads or tails, but not heads and tails.
The second of these dictates that either A or B must happen - no other outcomes are possible. You can flip a coin and get either heads or tails. No other outcomes are possible, so that (it is assumed) you cannot flip the coin and have it land on its edge.
All of these statements are summarised in the equation
\[P(A)+P(B)=1\]
.The definition of 'complementary events' only applies to two events, but we can apply similar conditions to mutually exclusive and exhaustive events. If events A, B, C are mutually exclusive and exhaustive then 1 and 2 become
1. A, B, C are mutually exclusive.
2. A, B, C are mutually exhaustive.
The equation becomes
\[P(A)+P(B)+P(C)=1\]
.