> For the complete documentation index, see [llms.txt](https://cs70.bencuan.me/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://cs70.bencuan.me/probability/discrete-probability.md).

# Discrete Probability

## Probability Basics

<http://prob140.org/textbook/content/Chapter_02/00_Calculating_Chances.html>

* [Adding and subtracting probabilities](http://prob140.org/textbook/content/Chapter_02/01_Addition.html) -[Multiplying probabilities: random draws without replacement, conditional probabilities](http://prob140.org/textbook/content/Chapter_02/03_Multiplication.html)

## Bayes' Rule

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

<http://prob140.org/textbook/content/Chapter_02/05_Updating_Probabilities.html#bayes-rule>

## Random Variables

### Probability Spaces

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

<http://prob140.org/textbook/content/Chapter_02/00_Calculating_Chances.html>

### 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>


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