{"schema":"https://ver.cy/schemas/card/1.0.0","id":"vr.tr.classical-definition-of-probability","code":"thing-q908596","url":"https://ver.cy/models/thing/q908596/","name":"classical definition of probability","alternateNames":[],"kind":"thing","status":"published","version":"0.1.0-research.1","language":"en","classifiers":{"family":"Thing Registry","category":"Information and virtual systems","entryKind":"thing","plane":"INF","domain":["INF.KNW"],"industry":[],"navPath":"","tags":[],"facets":{}},"whatItIs":"The classical definition of probability assigns an event the ratio of the number of elementary outcomes favourable to it to the total number of elementary outcomes in a finite, nonempty sample space whose outcomes are assumed equally likely.","purpose":"Enable an agent to recognise the classical definition of probability, assess whether its assumptions hold, and use favourable-to-total outcome counts without overstating their justification.","scope":{"in":["The relationship between elementary outcomes, events and the sample space","Finite outcome counts and the favourable-to-total ratio","Equiprobability assumptions and their supporting arguments","Counting conventions concerning order, replacement and distinguishability","Conditional restriction and changes in outcome representation","Applicability decisions and unresolved modelling assumptions"],"out":["Probability theory as a whole and its general axiomatic foundations","Long-run frequency as a definition of probability","Subjective degrees of belief and Bayesian inference frameworks","Continuous uniform distributions and geometric probability constructions","The physical design and empirical calibration of randomising devices","Combinatorics beyond the counting needed for a specified probability problem"],"boundaries":[]},"distinguishingFeatures":["A direct application requires a finite, nonempty set of elementary outcomes; counting favourable outcomes is insufficient without this requirement.","The ratio uses equally probable elementary outcomes, not merely outcomes assigned different names.","Equal likelihood is assumed or justified before the ratio is applied; observed relative frequency is not the definition.","An event may aggregate several elementary outcomes, so named events need not have equal probabilities.","Unlike a general axiomatic probability model, this definition determines probabilities from cardinalities once the uniform elementary representation is accepted."],"structure":{"bundles":[{"id":"finite-uniform-definition","name":"Finite uniform definition","description":"Records the mathematical objects and assumptions that make the classical ratio meaningful.","layers":[{"id":"elementary-outcome-space","name":"Elementary outcome space","description":"Identifies the experiment or abstract trial and its exhaustive, mutually exclusive elementary outcomes.","findings":[{"id":"finite-nonempty-space","name":"Finite nonempty space","description":"An application must identify Ω with a positive finite cardinality; its elementary outcomes must cover the trial without overlap.","questions":[{"text":"What trial is represented, and what makes two elementary outcomes distinct?","id":"finite-nonempty-space-q01","kind":"definition"},{"text":"How is it established that Ω is finite, nonempty, exhaustive and mutually exclusive?","id":"finite-nonempty-space-q02","kind":"boundary"}]}]},{"id":"event-and-ratio","name":"Event and ratio","description":"Connects an event membership rule to the classical probability calculation.","findings":[{"id":"favourable-total-ratio","name":"Favourable-to-total ratio","description":"For A ⊆ Ω under equiprobability, the classical definition assigns P(A) = |A|/|Ω|, including zero for the empty event and one for Ω.","questions":[{"text":"What exact rule determines whether an elementary outcome belongs to A?","id":"favourable-total-ratio-q01","kind":"definition"},{"text":"What are |A| and |Ω|, and what exact ratio follows from those counts?","id":"favourable-total-ratio-q02","kind":"measurement"}]}]}]},{"id":"equiprobability-warrant","name":"Equiprobability warrant","description":"Separates the equal-probability requirement from the arguments used to support it.","layers":[{"id":"equality-assumption","name":"Equality assumption","description":"Records whether uniformity is stipulated within a mathematical model or argued for a target process.","findings":[{"id":"basis-for-equal-likelihood","name":"Basis for equal likelihood","description":"Equiprobability needs an explicit basis; ignorance of differences alone does not establish that a physical process generates outcomes uniformly.","questions":[{"text":"Is equal likelihood stipulated, inferred from symmetry or supported as an empirical approximation?","id":"basis-for-equal-likelihood-q01","kind":"provenance"},{"text":"Which properties of the mechanism and outcome representation make that justification applicable?","id":"basis-for-equal-likelihood-q02","kind":"boundary"}]}]},{"id":"symmetry-and-challenge","name":"Symmetry and challenge","description":"Tests whether the proposed symmetry survives the details of the trial and available evidence.","findings":[{"id":"uniformity-challenge","name":"Uniformity challenge","description":"A symmetry argument must concern the probability-generating model, including relevant initial conditions and selection rules, rather than only the appearance or labels of outcomes.","questions":[{"text":"Which transformations exchange elementary outcomes while preserving the assumed trial conditions?","id":"uniformity-challenge-q01","kind":"definition"},{"text":"What evidence or mechanism detail would require withdrawing or qualifying the uniformity assumption?","id":"uniformity-challenge-q02","kind":"action"}]}]}]},{"id":"counting-and-representation","name":"Counting and representation","description":"Controls how outcomes are distinguished, counted and aggregated.","layers":[{"id":"counting-conventions","name":"Counting conventions","description":"Records order, replacement and distinguishability before choosing a counting method.","findings":[{"id":"consistent-counting-units","name":"Consistent counting units","description":"Numerator and denominator must count outcomes at the same resolution, with conventions matching the trial rather than chosen for convenience.","questions":[{"text":"Does the trial distinguish order and object identity, and does it permit replacement?","id":"consistent-counting-units-q01","kind":"definition"},{"text":"How can enumeration or a justified counting argument verify that neither count omits or duplicates elementary outcomes?","id":"consistent-counting-units-q02","kind":"action"}]}]},{"id":"aggregation-effects","name":"Aggregation effects","description":"Tracks what happens when elementary outcomes are grouped into coarser labels.","findings":[{"id":"unequal-aggregate-multiplicity","name":"Unequal aggregate multiplicity","description":"Under a uniform elementary model, a coarse outcome has probability proportional to the number of elementary outcomes mapped to it; for two independent fair six-sided dice, sums are therefore not equally probable.","questions":[{"text":"How many elementary outcomes map to each aggregate label used in the proposed calculation?","id":"unequal-aggregate-multiplicity-q01","kind":"measurement"},{"text":"Does the coarser representation preserve equal probabilities, or must its labels carry different weights?","id":"unequal-aggregate-multiplicity-q02","kind":"boundary"}]}]}]},{"id":"valid-use-and-limits","name":"Valid use and limits","description":"Determines which deductions remain justified and when the classical definition must give way to another model.","layers":[{"id":"conditioning-and-validation","name":"Conditioning and validation","description":"Handles restricted information and checks results against basic consequences of the model.","findings":[{"id":"conditional-counting","name":"Conditional counting","description":"Within a finite uniform model, conditioning on a nonempty event B gives P(A|B) = |A ∩ B|/|B|; evidence obtained through a selective reporting process may require modelling that process before treating it as simple restriction.","questions":[{"text":"Does the information establish an event B directly, or does an observation or reporting mechanism affect what was learned?","id":"conditional-counting-q01","kind":"boundary"},{"text":"What are |A ∩ B| and |B|, and is B nonempty?","id":"conditional-counting-q02","kind":"measurement"}]}]},{"id":"applicability-boundaries","name":"Applicability boundaries","description":"Identifies cases where raw finite cardinality ratios do not define the required probability.","findings":[{"id":"reject-unsupported-extension","name":"Reject unsupported extension","description":"Unequal elementary probabilities require weighted calculation; infinite spaces require a different construction rather than direct division of favourable and total cardinalities.","questions":[{"text":"Does the proposed application contain unequal elementary probabilities, infinitely many outcomes or unresolved sample-space choices?","id":"reject-unsupported-extension-q01","kind":"boundary"},{"text":"Should the agent refine the representation, request justification or refer the calculation to a weighted or measure-based probability model?","id":"reject-unsupported-extension-q02","kind":"action"}]}]}]},{"id":"evidence-and-external-alignment","name":"Evidence and external alignment","description":"What the world already says about this thing, gathered so the model can be checked against it.","layers":[{"id":"reported-evidence","name":"Reported evidence","description":"Findings from the breadth pass, kept separate from the structural claims.","findings":[{"id":"evidence-confidence-notes","name":"Check these first","description":"Recalled without web access and unsourced; every item is a lead to verify.","questions":[{"text":"Which of these check these first hold for the sense of classical definition of probability this model covers, and on what evidence?","id":"evidence-confidence-notes-q01","kind":"provenance"}]},{"id":"evidence-real-world-use","name":"Real-world use","description":"Recalled without web access and unsourced; every item is a lead to verify.","questions":[{"text":"Which of these real-world use hold for the sense of classical definition of probability this model covers, and on what evidence?","id":"evidence-real-world-use-q01","kind":"provenance"}]},{"id":"evidence-measurements","name":"Typical measurements","description":"Recalled without web access and unsourced; every item is a lead to verify.","questions":[{"text":"Which of these typical measurements hold for the sense of classical definition of probability this model covers, and on what evidence?","id":"evidence-measurements-q01","kind":"provenance"}]},{"id":"evidence-failure-modes-and-hazards","name":"Failure modes and hazards","description":"Recalled without web access and unsourced; every item is a lead to verify.","questions":[{"text":"Which of these failure modes and hazards hold for the sense of classical definition of probability this model covers, and on what evidence?","id":"evidence-failure-modes-and-hazards-q01","kind":"provenance"}]},{"id":"evidence-neighbours","name":"Neighbouring kinds and how to tell them apart","description":"Recalled without web access and unsourced; every item is a lead to verify.","questions":[{"text":"Which of these neighbouring kinds and how to tell them apart hold for the sense of classical definition of probability this model covers, and on what evidence?","id":"evidence-neighbours-q01","kind":"provenance"}]}]}]}]},"agentConduct":{"may":["Explain the classical definition and its assumption of equally likely outcomes.","Compute probabilities with it where the assumption is justified."],"mustNot":["Apply it where outcomes are not equally likely, such as loaded dice or real-world risks.","Present probabilities computed with it as certain predictions.","Use it to mislead people about odds in gambling or risk."],"requiresHuman":["Using probability estimates in decisions about people's health, money or safety."]},"ethics":{"considerations":["Misapplied probability can mislead people about risk and odds."],"affectedParties":["Students","Gamblers","People making risk decisions"]},"owners":{"steward":"Nobody owns it; it is a concept of probability theory.","roles":[],"masterSystems":[]},"relations":[{"target":"Q7246880","type":"parent","note":"registry parent class"}],"interaction":{"identity":{"applicability":"required","items":["Vercy registry: vr.tr.classical-definition-of-probability","Wikidata: Q908596 (https://www.wikidata.org/wiki/Q908596)"]},"properties":{"applicability":"not-applicable","items":["Sample-space cardinality: Positive integer count of elementary outcomes","Favourable-outcome cardinality: Integer from 0 to the sample-space cardinality","Equiprobability justification: Explicit mathematical stipulation; symmetry argument with stated assumptions; empirical support for approximation; unsupported assumption","Outcome representation: Ordered or unordered; distinguishable or indistinguishable; with or without replacement; other explicitly described representation","Event membership: A is a subset of Ω, defined by an explicit membership rule","Calculated probability: Dimensionless rational number in [0, 1]","Application status: Applicable within stated model; provisionally applicable to target process; assumptions unresolved; inapplicable"]},"recognition":{"applicability":"not-applicable","items":[]},"capabilities":{"applicability":"required","items":["Construct a finite elementary sample space and define the event to be evaluated.","Audit whether a symmetry or sampling argument supports equal probabilities.","Enumerate or count favourable and total outcomes using consistent conventions.","Calculate exact probabilities and conditional probabilities within an accepted uniform model.","Detect biased aggregation, double counting and unjustified equiprobability.","Explain why a proposed application needs additional assumptions or a different probability model."]},"hazards":{"applicability":"required","items":["Assuming equal likelihood without justification gives wrong probabilities.","Wrong odds can lead to harmful gambling or risk decisions."]},"interfaces":{"applicability":"not-applicable","items":[]},"context":{"applicability":"required","items":["The classical definition of probability is used in elementary probability theory and combinatorial problems with finite sample spaces.","It supports calculations for idealized games of chance and random selections when equally likely elementary outcomes are justified."]}},"sources":[{"title":"Wikidata item Q908596: classical definition of probability","url":"https://www.wikidata.org/wiki/Q908596","note":"identity and sense of the item"},{"title":"Wikipedia: Classical definition of probability","url":"https://en.wikipedia.org/wiki/Classical_definition_of_probability","note":"general description of the item"}],"openQuestions":["Does the registry intend only the finite equiprobable definition, or also the broader historical classical interpretation of probability?","Which primary or authoritative sources should anchor the wording and any attribution to particular historical authors?","How should this catalogue distinguish the classical definition from the principle of indifference without treating them as interchangeable?","Does an existing Vercy world model already own this concept, requiring a registry link rather than a separate publication?","What evidence standard should Vercy require before an agent treats a real process as approximately equiprobable?"],"resources":{"spec":"/models/things/publications/thing-q908596/spec.json"},"provenance":{"origin":"thing registry research (pass 2)","builtFrom":["models/things/publications/thing-q908596/spec.json"],"providers":["Codex"],"researchStatus":"unreviewed","generatedAt":"2026-09-12T08:43:34Z","builder":"tools/build_cards.py@1.0.0"},"completeness":{"sections":{"classifiers":"filled","whatItIs":"filled","purpose":"filled","distinguishingFeatures":"filled","structure":"filled","agentConduct":"filled","ethics":"filled","owners":"filled","relations":"filled","interaction.identity":"filled","interaction.properties":"not-applicable","interaction.recognition":"not-applicable","interaction.capabilities":"filled","interaction.hazards":"filled","interaction.interfaces":"not-applicable","interaction.context":"filled","sources":"filled"},"notes":{"_gate":"Published through the thing publication gate 1.0 on 2026-10-07T10:10:33+00:00: completeness 1.00; sense: Wikidata description; 2 live sources; review by codex: pass","interaction.properties":"Plane INF: no invented physical properties.","interaction.interfaces":"No regulatory requirement or technical standard is intrinsic to this mathematical definition.","interaction.recognition":"This mathematical concept has no physical appearance that distinguishes it from other probability definitions."},"score":1.0}}