여집합의_확률_증명

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여집합의 확률 공식 증명.
= Theorem =
For any event $A$ ,
$P(A^c)=1-P(A)$

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

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Up: [[여러가지증명]]
Up: [[여러가지증명]] [[집합set]]



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
$\displaystyle =P(A\cup A^c)$
$\displaystyle =P(A)+P(A^c)$