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Question 4906: Missing and Outside Elementary Outcomes

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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← Question derivation index · Original question batch

R0008-04906 · q-20261008-advance-20261011-r06-sample-space-0056

Original question and givens

Elementary outcomes are Fin(6)={0,…,5}. Candidate raw list=[0, 1, 2, 3, 4, -6]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

  • G001 — Elementary outcomes are Fin(6)={0,…,5}. Candidate raw list=[0, 1, 2, 3, 4, -6]. Give (missing elementary outcomes, listed values outside the space), deduplicated and increasing.

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

explicit finite possible-outcome protocol

After

no probability law,equiprobability or independence inferred

Conditions: none

These tasks list possible outcomes,recordings or event membership without assigning probabilities.All combinations being possible does not imply equiprobability or independence.

Step identifiers and dependencies

Rule: possible_outcomes_not_probabilities · Uses: G001

S002 · implies

Before

valid source outcome=0

After

listed=Yes

Conditions: none

Inspect every element of complete S for omissions;repeating another item cannot fill a gap.

Step identifiers and dependencies

Rule: source_outcome_inventory_row · Uses: G001, S001

S003 · implies

Before

valid source outcome=1

After

listed=Yes

Conditions: none

Inspect every element of complete S for omissions;repeating another item cannot fill a gap.

Step identifiers and dependencies

Rule: source_outcome_inventory_row · Uses: G001, S002

S004 · implies

Before

valid source outcome=2

After

listed=Yes

Conditions: none

Inspect every element of complete S for omissions;repeating another item cannot fill a gap.

Step identifiers and dependencies

Rule: source_outcome_inventory_row · Uses: G001, S003

S005 · implies

Before

valid source outcome=3

After

listed=Yes

Conditions: none

Inspect every element of complete S for omissions;repeating another item cannot fill a gap.

Step identifiers and dependencies

Rule: source_outcome_inventory_row · Uses: G001, S004

S006 · implies

Before

valid source outcome=4

After

listed=Yes

Conditions: none

Inspect every element of complete S for omissions;repeating another item cannot fill a gap.

Step identifiers and dependencies

Rule: source_outcome_inventory_row · Uses: G001, S005

S007 · implies

Before

valid source outcome=5

After

listed=No

Conditions: none

Inspect every element of complete S for omissions;repeating another item cannot fill a gap.

Step identifiers and dependencies

Rule: source_outcome_inventory_row · Uses: G001, S006

S008 · implies

Before

candidate list element=-6

After

inside S=No

Conditions: none

An outside-domain number in the candidate list is still not a possible outcome.

Step identifiers and dependencies

Rule: candidate_space_inventory_row · Uses: G001, S007

S009 · implies

Before

candidate list element=0

After

inside S=Yes

Conditions: none

An outside-domain number in the candidate list is still not a possible outcome.

Step identifiers and dependencies

Rule: candidate_space_inventory_row · Uses: G001, S008

S010 · implies

Before

candidate list element=1

After

inside S=Yes

Conditions: none

An outside-domain number in the candidate list is still not a possible outcome.

Step identifiers and dependencies

Rule: candidate_space_inventory_row · Uses: G001, S009

S011 · implies

Before

candidate list element=2

After

inside S=Yes

Conditions: none

An outside-domain number in the candidate list is still not a possible outcome.

Step identifiers and dependencies

Rule: candidate_space_inventory_row · Uses: G001, S010

S012 · implies

Before

candidate list element=3

After

inside S=Yes

Conditions: none

An outside-domain number in the candidate list is still not a possible outcome.

Step identifiers and dependencies

Rule: candidate_space_inventory_row · Uses: G001, S011

S013 · implies

Before

candidate list element=4

After

inside S=Yes

Conditions: none

An outside-domain number in the candidate list is still not a possible outcome.

Step identifiers and dependencies

Rule: candidate_space_inventory_row · Uses: G001, S012

S014 · implies

Before

S=[0, 1, 2, 3, 4, 5];normalized candidate list=[-6, 0, 1, 2, 3, 4]

After

([5], [-6])

Conditions: none

The first field lists omitted S-elements and the second lists outside entries;do not swap the two differences.

Step identifiers and dependencies

Rule: sample_list_two_sided_defects · Uses: G001, S013

Reverse checks

  • S014 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S013 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S012 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S011 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S010 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S009 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S008 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S007 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S006 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
  • S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

([5], [-6])

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: 397f94244fa19008a25327e8da3a971fb8534b5cbf0222ce58aca88428c38219
  • candidate record SHA-256: 4a6a927247b1d52ecfec1cd3a83c289ca18f0f67d247e7ccf447f641ec4a9224
  • semantic review receipt SHA-256: b6e05a3e8193a93db505dbf337528fca72e2e41528b1e92b698a3f0683d74289
  • question-first witness SHA-256: caa8693baf0b91acd09a20215d1aa6954ae513fc0b0814f26ac1c8c834b60d67
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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