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# Discrete Probability

## Bayes' Rule

Bayes' Rule is used to re-express conditional probabilities
$P(A|B)$
.

## Random Variables

### Probability Spaces

Probability spaces describe all of the possible values of a random variable, and how likely each of those outcomes are.

### Equality

Two variables are equal if
$X(\omega) = Y(\omega)$
for all
$\omega \in \Omega$
, where
$\Omega$
is a probability space (all possible values).
http://prob140.org/textbook/content/Chapter_03/03_Equality.html