The complement of an event $A$ is the set of all outcomes that is not $A$.

The complement of event $A$ is expressed as $\stackrel{‾}{A}$ ($A$ 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).

$\begin{array}{rl}\mathbb{P}\left(A\right)+\mathbb{P}\left(\stackrel{‾}{A}\right)& =1\\ \mathbb{P}\left(\stackrel{‾}{A}\right)& =1-\mathbb{P}\left(A\right)\end{array}$

Examples:

• When tossing a fair six-sided die, the probability of not getting a 5 would be

$\begin{array}{rl}\mathbb{P}\left(\stackrel{‾}{"5"}\right)& =1-\mathbb{P}\left("5"\right)\\ & =1-\frac{1}{6}\\ & =\frac{5}{6}\end{array}$
• When drawing a card from a deck of 52 playing cards, the probability of getting "not King" is

$\begin{array}{rl}\mathbb{P}\left(\stackrel{‾}{"King"}\right)& =1-\mathbb{P}\left("King"\right)\\ & =1-\frac{4}{52}\\ & =\frac{48}{52}\\ & =\frac{12}{13}\end{array}$