classical definition of probability

Finite nonempty space

An application must identify Ω with a positive finite cardinality; its elementary outcomes must cover the trial without overlap.

1. What trial is represented, and what makes two elementary outcomes distinct? definition
2. How is it established that Ω is finite, nonempty, exhaustive and mutually exclusive? boundary

Favourable-to-total ratio

For A ⊆ Ω under equiprobability, the classical definition assigns P(A) = |A|/|Ω|, including zero for the empty event and one for Ω.

1. What exact rule determines whether an elementary outcome belongs to A? definition
2. What are |A| and |Ω|, and what exact ratio follows from those counts? measurement

Basis for equal likelihood

Equiprobability needs an explicit basis; ignorance of differences alone does not establish that a physical process generates outcomes uniformly.

1. Is equal likelihood stipulated, inferred from symmetry or supported as an empirical approximation? provenance
2. Which properties of the mechanism and outcome representation make that justification applicable? boundary

Uniformity challenge

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.

1. Which transformations exchange elementary outcomes while preserving the assumed trial conditions? definition
2. What evidence or mechanism detail would require withdrawing or qualifying the uniformity assumption? action

Consistent counting units

Numerator and denominator must count outcomes at the same resolution, with conventions matching the trial rather than chosen for convenience.

1. Does the trial distinguish order and object identity, and does it permit replacement? definition
2. How can enumeration or a justified counting argument verify that neither count omits or duplicates elementary outcomes? action

Unequal aggregate multiplicity

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.

1. How many elementary outcomes map to each aggregate label used in the proposed calculation? measurement
2. Does the coarser representation preserve equal probabilities, or must its labels carry different weights? boundary

Conditional counting

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.

1. Does the information establish an event B directly, or does an observation or reporting mechanism affect what was learned? boundary
2. What are |A ∩ B| and |B|, and is B nonempty? measurement

Reject unsupported extension

Unequal elementary probabilities require weighted calculation; infinite spaces require a different construction rather than direct division of favourable and total cardinalities.

1. Does the proposed application contain unequal elementary probabilities, infinitely many outcomes or unresolved sample-space choices? boundary
2. Should the agent refine the representation, request justification or refer the calculation to a weighted or measure-based probability model? action

Check these first

Recalled without web access and unsourced; every item is a lead to verify.

1. Which of these check these first hold for the sense of classical definition of probability this model covers, and on what evidence? provenance

Real-world use

Recalled without web access and unsourced; every item is a lead to verify.

1. Which of these real-world use hold for the sense of classical definition of probability this model covers, and on what evidence? provenance

Typical measurements

Recalled without web access and unsourced; every item is a lead to verify.

1. Which of these typical measurements hold for the sense of classical definition of probability this model covers, and on what evidence? provenance

Failure modes and hazards

Recalled without web access and unsourced; every item is a lead to verify.

1. Which of these failure modes and hazards hold for the sense of classical definition of probability this model covers, and on what evidence? provenance

Neighbouring kinds and how to tell them apart

Recalled without web access and unsourced; every item is a lead to verify.

1. 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? provenance