# Question 35580: Completeness of a Finite Sample Space [Return to catalogue page 178](https://ocme.evemisslab.com/en/questions/page/178/) [← Question derivation index](https://ocme.evemisslab.com/en/questions/) · [Original question batch](https://ocme.evemisslab.com/en/practice/batch-20260914-domain-foundations/#q-20260914-finite-sample-space-completeness-0005) This teaching derivation has second-context AI mathematical and bilingual semantic review, limited to the model and assumptions stated in this question. It has no human review or new Lean proof and does not promote the original question or MKO to Canonical truth. R0070-35580 · q-20260914-finite-sample-space-completeness-0005 ## Original question and givens The experiment is one draw from explicitly labelled cards with elementary outcomes label 41, label 42. At this observation scale the candidate sample space is S={label 42}. Is it complete? - G001 — The experiment is one draw from explicitly labelled cards with elementary outcomes label 41, label 42. At this observation scale the candidate sample space is S={label 42}. 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. - [mko-sample-space](https://ocme.evemisslab.com/en/mko/mko-sample-space/) ## Step-by-step derivation S001 · impliesBefore 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 dependenciesRule: R70_SOURCE_bank_specific_interface · Uses: G001 S002 · impliesBefore source roles = [one reading of the declared labelled cards label 41、label 42, one declared finite trial, [label 41, label 42], [label 42]] 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 dependenciesRule: Sample_GIVEN_complete_elementary_outcomes_at_declared_scale · Uses: G001, S001 S003 · impliesBefore source roles = [label 41, [label 42]] After derived = [No] Conditions: none Check EACH required outcome for inclusion;all listed outcomes being legal does not rule out a missing one. Step identifiers and dependenciesRule: Sample_EACH_expected_outcome_is_listed · Uses: G001, S002 S004 · impliesBefore source roles = [label 42, [label 42]] 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 dependenciesRule: Sample_EACH_expected_outcome_is_listed · Uses: G001, S003 S005 · impliesBefore source roles = [label 42, [label 41, label 42]] 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 dependenciesRule: Sample_EACH_listed_outcome_is_possible · Uses: G001, S004 S006 · impliesBefore source roles = [[label 41], [], missing_outcome] After derived = [No] 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 dependenciesRule: Sample_BOTH_inclusions_and_postderived_mode · Uses: G001, S005 ## Reverse checks - 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 No 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: bfe4ae2822154c0c04f868348cd74b00ddc605f007ecdff70b3e6347f4d7f9b0 - candidate record SHA-256: 54a380d082216a3a5923ad65678c64c29b1b5530f04ad8cdb4e31bf420e860d3 - semantic review receipt SHA-256: 9820ac6529139bd53d516c8bfdfdd41184b0cd52dad69fa433344010db37af80 - question-first witness SHA-256: c9c939762bbd4d3ea3403084c8e95541dc2c7e56eb82fc74eaba8c80a4517dab - Lean: NOT_RUN · human review: NOT_PERFORMED [Same-source full JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20260914-finite-sample-space-completeness-0005.json)