See also: numbers, Permutations and Combinations

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

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

$$\begin{array}{rl}\mathbb{P}(A)+\mathbb{P}(\bar{A})& =1\\ \mathbb{P}(\bar{A})& =1-\mathbb{P}(A)\end{array}$$

Examples:

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

  $$\begin{array}{rl}\mathbb{P}(\overline{''5''})& =1-\mathbb{P}(''5'')\\ & =1-\frac{1}{6}\\ & =\frac{5}{6}\end{array}$$

• When drawing a card from a deck of 52 playing cards, the probability of getting "not King" is

  $$\begin{array}{rl}\mathbb{P}(\overline{''King''})& =1-\mathbb{P}(''King'')\\ & =1-\frac{4}{52}\\ & =\frac{48}{52}\\ & =\frac{12}{13}\end{array}$$

By Jimmy Sie

See also: numbers, Permutations and Combinations