# Probability
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## Microsims — p5.js
### Probability (p5.js) · `P(A)`
<div class="microsim-player">
<iframe src="https://editor.p5js.org/sciencenibber/full/IOMm0e1Kk" width="100%" height="480" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Probability — p5.js microsim"></iframe>
</div>
*The mathematics of chance — the foundation for treating noise and random signals.*
**Open in the editor:** [▶ fork this sketch](https://editor.p5js.org/sciencenibber/sketches/IOMm0e1Kk) · movement *IX · Foundations & the rest of the toolbox* · library `p5js`
### Related microsims
Live sims on neighbouring articles — 2 of them inside this article's own Wikipedia link tree:
- [[Chaos_theory]] *(in tree)*
- [[Graph_theory]] *(in tree)*
- [[Analog_signal]]
- [[Autocorrelation]]
- [[Bifurcation_theory]]
- [[Calculus]]
*Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*
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## Links (Wikipedia order)
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`Abductive_reasoning` · `Abraham_de_Moivre` · `Actuarial_science` · `Adolphe_Quetelet` · `Adrien-Marie_Legendre` · `Albert_Einstein` · `Almost_surely` · `Analytic–synthetic_distinction` · `Andrey_Kolmogorov` · `Andrey_Markov` · `Antecedent_(logic)` · `Antinomy` · `Argumentation_theory` · `Ars_Conjectandi` · `Artemas_Martin` · [[Artificial_intelligence]] · `Augustus_De_Morgan` · `Aumann's_agreement_theorem` · `Authority` · `Avogadro_constant` · `BBC` · `Bayes'_theorem` · `Bayesian_probability` · `Bernoulli_distribution` · `Bernoulli_process` · `Bernoulli_trial` · `Binomial_distribution` · `Blaise_Pascal` · `Boole's_inequality` · `Bruno_de_Finetti` · `Cache_language_model` · `Cambridge_University_Press` · `Carl_Friedrich_Gauss` · `Catalog_of_articles_in_probability_theory` · [[Chaos_theory]] · [[Christiaan_Huygens]] · `Christian_August_Friedrich_Peters` · `Classical_logic` · `Collectively_exhaustive_events` · `Complementary_event` · `Computational_logic` · [[Computer_science]] · `Conditional_independence` · `Conditional_probability` · `Consequent` · `Contingency_(philosophy)` · `Continuous_or_discrete_variable` · `Continuous_uniform_distribution` · `Contradiction` · `Copenhagen_interpretation` · `Cox's_theorem` · `Credence_(statistics)` · `Critical_thinking` · `Daniel_Bernoulli` · `Deductive_closure` · [[Deductive_reasoning]] · `Definition` · `Dempster–Shafer_theory` · `Description` · `Determinism` · `Deterministic_system` · `Dichotomy` · `Edwin_Thompson_Jaynes` · `Elementary_event` · `Empirical_evidence` · `Empirical_probability` · [[Engineering]] · `Equiprobability` · `Erwin_Schrödinger` · `Etymology` · `Eudaemons` · `Event_(probability_theory)` · [[Expected_value]] · `Experiment` · `Experiment_(probability_theory)` · `Exponential_distribution` · `Finance` · `Financial_regulation` · `Formal_proof` · `Formal_semantics_(natural_language)` · `Frequency_(statistics)` · `Frequentist_probability` · `Function_(mathematics)` · `Fuzzy_logic` · `GNU_Free_Documentation_License` · `Gambling` · [[Game_theory]] · `Genetics_(journal)` · `Genetics_Society_of_America` · [[George_Boole]] · `Gerolamo_Cardano` · `Giovanni_Schiaparelli` · `Glossary_of_Arabic_toponyms` · `Glossary_of_Hebrew_toponyms` · [[Glossary_of_aerospace_engineering]] · `Glossary_of_agriculture` · `Glossary_of_archaeology` · `Glossary_of_architecture` · `Glossary_of_areas_of_mathematics` · `Glossary_of_artificial_intelligence` · `Glossary_of_astronomy` · `Glossary_of_biology` · `Glossary_of_bird_terms` · `Glossary_of_botanical_terms` · `Glossary_of_calculus` · `Glossary_of_cellular_and_molecular_biology_(0–L)` · `Glossary_of_cellular_and_molecular_biology_(M–Z)` · `Glossary_of_chemistry_terms` · [[Glossary_of_civil_engineering]] · `Glossary_of_clinical_research` · `Glossary_of_computer_hardware_terms` · `Glossary_of_computer_science` · `Glossary_of_developmental_biology` · `Glossary_of_ecology` · `Glossary_of_economics` · [[Glossary_of_electrical_and_electronics_engineering]] · `Glossary_of_engineering:_A–L` · `Glossary_of_engineering:_M–Z` · `Glossary_of_entomology_terms` · `Glossary_of_environmental_science` · `Glossary_of_genetics_and_evolutionary_biology` · `Glossary_of_geography_terms_(A–M)` · `Glossary_of_geography_terms_(N–Z)` · `Glossary_of_geology` · `Glossary_of_ichthyology` · `Glossary_of_machine_vision` · [[Glossary_of_mechanical_engineering]] · `Glossary_of_medicine` · `Glossary_of_meteorology` · `Glossary_of_mycology` · `Glossary_of_nanotechnology` · `Glossary_of_physics` · `Glossary_of_probability_and_statistics` · `Glossary_of_protistology` · `Glossary_of_psychiatry` · `Glossary_of_quantum_computing` · `Glossary_of_robotics` · `Glossary_of_scientific_naming` · [[Glossary_of_structural_engineering]] · `Glossary_of_virology` · [[Graph_theory]] · `Groupthink` · `Heuristic_(psychology)` · `History_of_logic` · `History_of_probability` · `History_of_statistics` · `Ian_Hacking` · `In_Our_Time_(radio_series)` · `Independence_(probability_theory)` · `Indeterminism` · [[Inductive_reasoning]] · `Inference` · `Informal_logic` · `Instrumentalism` · `Integral_geometry` · `Internet_Encyclopedia_of_Philosophy` · `Inverse_probability` · `Italians` · `James_Franklin_(philosopher)` · `James_Ivory_(mathematician)` · `James_Whitbread_Lee_Glaisher` · `John_E._Freund` · `John_Herschel` · `Joint_probability_distribution` · `Journal_of_the_American_Statistical_Association` · `Karl_Pearson` · [[Kinetic_theory_of_gases]] · `Laplace's_demon` · `Law_of_large_numbers` · `Law_of_total_probability` · `Likelihood_function` · `Linguistic_entailment` · `List_of_Boolean_algebra_topics` · `List_of_fallacies` · `List_of_logic_symbols` · `List_of_logicians` · `List_of_mathematical_logic_topics` · `List_of_mathematical_probabilists` · `List_of_paradoxes` · `List_of_probability_journals` · `List_of_rules_of_inference` · `List_of_set_theory_topics` · [[Logic]] · `Logic_in_computer_science` · `Logical_consequence` · `Logical_form` · `Logical_truth` · [[Machine_learning]] · `Marginal_distribution` · `Market_(economics)` · `Markov_chain` · `Mathematical_logic` · `Mathematics` · `Max_Born` · `Measure_(mathematics)` · `Metalogic` · `Metamathematics` · `Morgan_Crofton` · `Mutual_exclusivity` · `Name` · `Natural_language_processing` · [[Necessity_and_sufficiency]] · `Nobility` · `Non-classical_logic` · `Normal_distribution` · `Notation_in_probability_and_statistics` · `Odds` · `Oikonyms_in_West_and_South_Asia` · `Olav_Kallenberg` · `Outcome_(probability)` · `Outline_of_logic` · `Outline_of_probability` · `Paradox` · `Pareto_distribution` · `Philosophical_logic` · `Philosophy` · `Philosophy_of_logic` · [[Physics]] · `Pierre-Simon_Laplace` · `Pierre_de_Fermat` · `Poisson_distribution` · `Possibility_theory` · `Power_set` · `Premise` · `Probability_(disambiguation)` · `Probability_axioms` · `Probability_distribution` · `Probability_interpretations` · `Probability_measure` · `Probability_space` · `Probability_theory` · `Probable_error` · `Propensity_probability` · [[Proposition]] · `Quantum_decoherence` · `Quantum_fluctuation` · [[Quantum_mechanics]] · `Random_variable` · `Random_walk` · `Randomness` · `Real_number` · `Reality` · `Realization_(probability)` · `Reason` · `Reference` · `Reliability_(statistics)` · `Richard_Dedekind` · `Richard_Jeffrey` · `Richard_Threlkeld_Cox` · `Risk` · `Robert_Adrain` · `Robert_Leslie_Ellis` · `Roger_Cotes` · `Roulette` · `Sample_space` · [[Schrödinger_equation]] · [[Science]] · `Set_(mathematics)` · [[Set_theory]] · `Singleton_(mathematics)` · `Statistical_inference` · `Statistical_model` · `Statistics` · `Stochastic` · `Stochastic_process` · `Substitution_(logic)` · `Syntax_(logic)` · `The_Doctrine_of_Chances` · `Theory` · `Thomas_Simpson` · `Tree_diagram_(probability_theory)` · `Truth` · `Undefined_(mathematics)` · `Validity_(logic)` · `Variance` · `Venn_diagram` · `Warranty` · `Wave_function` · `Wave_function_collapse` · [[Wayback_Machine]] · `Well-defined_expression` · `William_Fishburn_Donkin` · `Witness` · `Σ-algebra`
> Signal Processing concept · part of the Signal Processing Portal · movement IX · !09 解析 kaiseki.svg
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!480
*Rendered from the live microsim (▶ motion).*
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## Images
<figure class="wt-gifplate">
<img src="https://commons.wikimedia.org/wiki/Special:FilePath/Monte_Carlo.gif" alt="Random Sampling" loading="lazy" decoding="async">
<figcaption><strong>Random Sampling</strong> — Show probability distributions emerging from random samples.<br>
<span class="wt-credit">Wikimedia Commons · <strong>licence pending verification</strong> (run <code>g17_gif_verify.py</code> on a networked lane) · <a href="https://commons.wikimedia.org/wiki/File:Monte_Carlo.gif">Details</a></span></figcaption>
</figure>
*Still companion to the 1 live microsim above: the sim is the instrument, the plate is the glance. §15 keeps the player first; this sits in the image slot on [[Probability]].*
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## See it next
[](Probability_density_function)
*→ [[Probability_density_function|Probability density function]]*
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---
Back to Signal Processing Portal · the room · Semiotic gateway
## What it is
Probability is the branch of mathematics quantifying uncertainty, assigning numbers between 0 and 1 to events and providing the axiomatic framework (measure theory) for random phenomena.
## How it works / why it matters
Signal processing treats noise, measurement error, and many real-world signals as random processes, so probability supplies the language for detection, estimation, and inference. Concepts such as expectation, variance, conditional probability, and stochastic processes let engineers derive optimal filters (e.g. Wiener and Kalman filters), characterize signal-to-noise ratio, and reason about the likelihood of correct decisions under uncertainty.
## Signs & universals
Instantiates:
- probability
- noise
- measurement
## Related
[[Probability_density_function]] · [[Information_theory]] · [[Signal-to-noise_ratio]] · Noise (physics) · [[Autocorrelation]] · Signal Processing
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*Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*
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## Wikipedia : Wikitube
**Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Probability) : [Wikitube](https://en.wikitube.io/wiki/Probability)
## Previous hub tags
Tree parents: [[Decision_theory]] · [[Dynamical_system]] · [[Emergence]] · [[Game_theory]] · [[Graph_theory]] · [[Information_theory]] · [[Monte_Carlo_method]] · [[Operations_research]] · [[Reliability_engineering]].
Legacy hubs: none.
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*Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*