여집합의_확률_증명

여집합의 확률 공식 증명.

Theorem

For any event $\displaystyle A$ ,
$\displaystyle P(A^c)=1-P(A)$

Proof

$\displaystyle 1 = P(S)$ (by axiom of probability) // 확률공리,probability_axiom later
$\displaystyle =P(A\cup A^c)$
$\displaystyle =P(A)+P(A^c)$