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Question 35582: Completeness of a Finite Sample Space

On this page
  1. Original question and givens
  2. Definition and scope
  3. Step-by-step derivation
  4. Reverse checks
  5. Result
  6. This question review and source binding

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R0070-35582 · q-20260914-finite-sample-space-completeness-0007

Original question and givens

The experiment is one draw from explicitly labelled cards with elementary outcomes label 61, label 62, label 63, label 64. At this observation scale the candidate sample space is S={label 61, label 62, label 63, label 64}. Is it complete?

  • G001 — The experiment is one draw from explicitly labelled cards with elementary outcomes label 61, label 62, label 63, label 64. At this observation scale the candidate sample space is S={label 61, label 62, label 63, label 64}. Is it complete?

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

Step-by-step derivation

S001 · implies

Before

source roles = [qf-finite-sample-space-completeness, [expected_outcomes, experiment, listed_outcomes, mode, observation_scale]]

After

derived = [sample, null, null]

Conditions: none

Use THIS bank’s actual fields,operation/domain and types.BASE retains permissible extra metadata.Do not import LDL SAFE/set limits or a different bank’s deduplication rules.

Step identifiers and dependencies

Rule: R70_SOURCE_bank_specific_interface · Uses: G001

S002 · implies

Before

source roles = [one reading of the declared labelled cards label 61、label 62、label 63、label 64, one declared finite trial, [label 61, label 62, label 63, label 64], [label 61, label 62, label 63, label 64]]

After

derived = [completeness only]

Conditions: none

A is GIVEN as the COMPLETE elementary-outcome list at the declared observation scale.Check whether B is exactly A;do not infer the universe from partial observations or assign equal likelihood/probabilities.

Step identifiers and dependencies

Rule: Sample_GIVEN_complete_elementary_outcomes_at_declared_scale · Uses: G001, S001

S003 · implies

Before

source roles = [label 61, [label 61, label 62, label 63, label 64]]

After

derived = [Yes]

Conditions: none

Check EACH required outcome for inclusion;all listed outcomes being legal does not rule out a missing one.

Step identifiers and dependencies

Rule: Sample_EACH_expected_outcome_is_listed · Uses: G001, S002

S004 · implies

Before

source roles = [label 62, [label 61, label 62, label 63, label 64]]

After

derived = [Yes]

Conditions: none

Check EACH required outcome for inclusion;all listed outcomes being legal does not rule out a missing one.

Step identifiers and dependencies

Rule: Sample_EACH_expected_outcome_is_listed · Uses: G001, S003

S005 · implies

Before

source roles = [label 63, [label 61, label 62, label 63, label 64]]

After

derived = [Yes]

Conditions: none

Check EACH required outcome for inclusion;all listed outcomes being legal does not rule out a missing one.

Step identifiers and dependencies

Rule: Sample_EACH_expected_outcome_is_listed · Uses: G001, S004

S006 · implies

Before

source roles = [label 64, [label 61, label 62, label 63, label 64]]

After

derived = [Yes]

Conditions: none

Check EACH required outcome for inclusion;all listed outcomes being legal does not rule out a missing one.

Step identifiers and dependencies

Rule: Sample_EACH_expected_outcome_is_listed · Uses: G001, S005

S007 · implies

Before

source roles = [label 61, [label 61, label 62, label 63, label 64]]

After

derived = [Yes]

Conditions: none

Check EACH listed outcome against the GIVEN universe;absence of omissions does not rule out impossible extras.

Step identifiers and dependencies

Rule: Sample_EACH_listed_outcome_is_possible · Uses: G001, S006

S008 · implies

Before

source roles = [label 62, [label 61, label 62, label 63, label 64]]

After

derived = [Yes]

Conditions: none

Check EACH listed outcome against the GIVEN universe;absence of omissions does not rule out impossible extras.

Step identifiers and dependencies

Rule: Sample_EACH_listed_outcome_is_possible · Uses: G001, S007

S009 · implies

Before

source roles = [label 63, [label 61, label 62, label 63, label 64]]

After

derived = [Yes]

Conditions: none

Check EACH listed outcome against the GIVEN universe;absence of omissions does not rule out impossible extras.

Step identifiers and dependencies

Rule: Sample_EACH_listed_outcome_is_possible · Uses: G001, S008

S010 · implies

Before

source roles = [label 64, [label 61, label 62, label 63, label 64]]

After

derived = [Yes]

Conditions: none

Check EACH listed outcome against the GIVEN universe;absence of omissions does not rule out impossible extras.

Step identifiers and dependencies

Rule: Sample_EACH_listed_outcome_is_possible · Uses: G001, S009

S011 · implies

Before

source roles = [[], [], complete]

After

derived = [Yes]

Conditions: none

Completeness requires BOTH inclusions.If both omissions and extras occur,the answer remains No;the source mode prioritizes omissions.Check mode only AFTER set comparison.

Step identifiers and dependencies

Rule: Sample_BOTH_inclusions_and_postderived_mode · Uses: G001, S010

Reverse checks

  • S011 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.
  • S010 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.
  • S009 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.
  • S008 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.
  • S007 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.
  • S006 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.
  • S005 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.
  • S004 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.
  • S003 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.
  • S002 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.
  • S001 · premise_and_result_audit — Reverse-audit THIS question’s original operands,roles and necessary premises;reconstruct the next step,without reversing a one-way implication.Numerical/finite-table checking is not formal proof of an arbitrary theorem.Original Q,bilingual sources,MKO,AST,status and history remain preserved.

Result

Yes

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.

Source hashes and review receipts
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: f1bc976b3c80727ee4b8da70e9c7005868b75e32263bbb396025f66379dbdba6
  • candidate record SHA-256: 10910ce0cff8c92e6babfb74c1d634919132b7700bf3f999982871ecdece73dd
  • semantic review receipt SHA-256: 9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80
  • question-first witness SHA-256: c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dab
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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