Probability Theory
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[(Up)](../../README.md#topics) | _See also: [Mathematics](../Mathematics/README.md#mathematics)_

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### Web resources

### Foundations

[Kolmogorov axioms - Wikipedia](https://en.wikipedia.org/wiki/Kolmogorov_axioms)

### Basic Questions

[Is probability physical or idealistic? Is probability an inherent part of nature/reality?](https://philosophy.stackexchange.com/questions/113570/is-probability-physical-or-idealistic-is-probability-an-inherent-part-of-nature) ★

[probability - In a family with two children, what are the chances, if one of the children is a girl, that both children are girls? - Mathematics Stack Exchange](https://math.stackexchange.com/questions/15055/in-a-family-with-two-children-what-are-the-chances-if-one-of-the-children-is-a/15085#15085) ★★★

[probability - A and B are independent. Does P(A ∩ B\|C) = P(A\|C) · P(B\|C) hold? - Cross Validated](https://stats.stackexchange.com/questions/639166/a-and-b-are-independent-does-pa-%e2%88%a9-bc-pac-pbc-hold) ★★★

[lattices made by \$a\\wedge b = ab\$ and \$a\\vee b=a+b-ab\$ - Mathematics Stack Exchange](https://math.stackexchange.com/questions/1228187/lattices-made-by-a-wedge-b-ab-and-a-vee-b-ab-ab) ★

[Q: Is it possible to choose an item from an infinite set of items such that each one has an equal chance of being selected? | Ask a Mathematician / Ask a Physicist](https://www.askamathematician.com/2010/01/q-is-it-possible-to-choose-an-item-from-an-infinite-set-of-items-such-that-each-one-has-an-equal-chance-of-being-selected/) ★★★

[probability theory - Is the Axiom of Choice inconsistent with Countable Additivity? - Mathematics Stack Exchange](https://math.stackexchange.com/questions/4862926/is-the-axiom-of-choice-inconsistent-with-countable-additivity) ★

### Conditional Probability

[Conditioning (probability) - Wikipedia](https://en.wikipedia.org/wiki/Conditioning_%28probability%29)

[Conditional probability - Wikipedia](https://en.wikipedia.org/wiki/Conditional_probability)

[Law of total probability - Wikipedia](https://en.wikipedia.org/wiki/Law_of_total_probability)

[Chain rule (probability) - Wikipedia](https://en.wikipedia.org/wiki/Chain_rule_%28probability%29)

### Bayesian Probability

[probability - Do Bayesians accept Kolmogorov\'s axioms? - Cross Validated](https://stats.stackexchange.com/questions/126056/do-bayesians-accept-kolmogorovs-axioms) ★★★

[bayesian probability and measure theory - Mathematics Stack Exchange](https://math.stackexchange.com/questions/2310252/bayesian-probability-and-measure-theory) ★

### Stochastic Processes

[Does the law of large numbers explain why quantum mechanics leads to statistical regularities? - Philosophy Stack Exchange](https://philosophy.stackexchange.com/questions/104871/does-the-law-of-large-numbers-explain-why-quantum-mechanics-leads-to-statistical) ★

[stochastic calculus - Why is Brownian motion useful in finance? - Quantitative Finance Stack Exchange](https://quant.stackexchange.com/questions/50167/why-is-brownian-motion-useful-in-finance) ★

### Algebraic Probability

[Algebraic Probability -- Almost Sure](https://almostsuremath.com/2019/11/10/algebraic-probability/) ★

[254A, Notes 5: Free probability \| What\'s new](https://terrytao.wordpress.com/2010/02/10/245a-notes-5-free-probability/) ★

_(in [Mathematics](../Mathematics/README.md#mathematics))_ [Readings | Mathematics for Computer Science | Electrical Engineering and Computer Science | MIT OpenCourseWare](https://ocw.mit.edu/courses/6-042j-mathematics-for-computer-science-fall-2010/pages/readings/) ★★


### Papers

[Probability Theory without Bayes\' Rule](https://arxiv.org/abs/1411.7920) ★

_(in [Order Theory](../Order%20Theory/README.md#order-theory))_ Deriving Laws from Ordering Relations (online @ [archive.org](https://archive.org/details/NASA_NTRS_Archive_20030107662)) ★★★ [💭](commentary/Chris%20Pressey.md#deriving-laws-from-ordering-relations)


### Books

Probability, Statistics, and Data (online @ [mathstat.slu.edu](https://mathstat.slu.edu/~speegle/_book/)) ★ [💭](commentary/Chris%20Pressey.md#probability-statistics-and-data)

Probability Theory (Jaynes) (online @ [www.med.mcgill.ca](http://www.med.mcgill.ca/epidemiology/hanley/bios601/GaussianModel/JaynesProbabilityTheory.pdf), [bayes.wustl.edu](https://bayes.wustl.edu/etj/prob/book.pdf), [archive.org](https://archive.org/details/jaynes-probability-theory), [archive.org](https://archive.org/details/jaynes-probability-theory_202409)) ★★★ [💭](commentary/Chris%20Pressey.md#probability-theory-jaynes)