See also: numbers, Permutations and Combinations
The complement of an event $A$ is the set of all outcomes that is not $A$.
The complement of event $A$ is expressed as $\stackrel{\u203e}{A}$ ($A$ bar) or ${A}^{c}$.
The probability of an event and its complement always add up to 1 (An event either occurs or it doesn't occur).
$$\begin{array}{rl}\mathbb{P}(A)+\mathbb{P}(\stackrel{\u203e}{A})& =1\\ \mathbb{P}(\stackrel{\u203e}{A})& =1-\mathbb{P}(A)\end{array}$$Examples:
When tossing a fair six-sided die, the probability of not getting a 5 would be
$$\begin{array}{rl}\mathbb{P}(\stackrel{\u203e}{''5''})& =1-\mathbb{P}(''5'')\\ & =1-\frac{1}{6}\\ & =\frac{5}{6}\end{array}$$When drawing a card from a deck of 52 playing cards, the probability of getting "not King" is
$$\begin{array}{rl}\mathbb{P}(\stackrel{\u203e}{''King''})& =1-\mathbb{P}(''King'')\\ & =1-\frac{4}{52}\\ & =\frac{48}{52}\\ & =\frac{12}{13}\end{array}$$See also: numbers, Permutations and Combinations