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Question 4928: All Ordered 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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R0008-04928 · q-20261008-advance-20261011-r06-sample-space-0003

Original question and givens

First-stage outcomes A=[-2, 2], second-stage outcomes B=[-1, 0, 3]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

  • G001 — First-stage outcomes A=[-2, 2], second-stage outcomes B=[-1, 0, 3]; every pair is allowed. Normalize and sort each axis, then list all ordered pairs with A as the outer loop and B as the inner loop.

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

first-stage outcome=-2;second-stage outcome=-1

After

[-2, -1]

Conditions: none

Enumerate with A as the outer loop and B as the inner loop;stage order matters.

Step identifiers and dependencies

Rule: ordered_outcome_pair · Uses: G001, S001

S003 · implies

Before

first-stage outcome=-2;second-stage outcome=0

After

[-2, 0]

Conditions: none

Enumerate with A as the outer loop and B as the inner loop;stage order matters.

Step identifiers and dependencies

Rule: ordered_outcome_pair · Uses: G001, S002

S004 · implies

Before

first-stage outcome=-2;second-stage outcome=3

After

[-2, 3]

Conditions: none

Enumerate with A as the outer loop and B as the inner loop;stage order matters.

Step identifiers and dependencies

Rule: ordered_outcome_pair · Uses: G001, S003

S005 · implies

Before

first-stage outcome=2;second-stage outcome=-1

After

[2, -1]

Conditions: none

Enumerate with A as the outer loop and B as the inner loop;stage order matters.

Step identifiers and dependencies

Rule: ordered_outcome_pair · Uses: G001, S004

S006 · implies

Before

first-stage outcome=2;second-stage outcome=0

After

[2, 0]

Conditions: none

Enumerate with A as the outer loop and B as the inner loop;stage order matters.

Step identifiers and dependencies

Rule: ordered_outcome_pair · Uses: G001, S005

S007 · implies

Before

first-stage outcome=2;second-stage outcome=3

After

[2, 3]

Conditions: none

Enumerate with A as the outer loop and B as the inner loop;stage order matters.

Step identifiers and dependencies

Rule: ordered_outcome_pair · Uses: G001, S006

S008 · implies

Before

A=[-2, 2];B=[-1, 0, 3]

After

[[-2, -1], [-2, 0], [-2, 3], [2, -1], [2, 0], [2, 3]]

Conditions: none

After deduplication,pair each A-value with each B-value exactly once to list the protocol's full Cartesian product.

Step identifiers and dependencies

Rule: complete_cartesian_outcome_protocol · Uses: G001, S007

Reverse checks

  • 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

[[-2, -1], [-2, 0], [-2, 3], [2, -1], [2, 0], [2, 3]]

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: 7f2a0a92648f4c49b16bca101fc4583d2f87a115b9a2e5bc4dccaef834803f53
  • candidate record SHA-256: 82c4a0275af93033010c39b05d276bde5a33afe646753bc36e679001c9589d9e
  • semantic review receipt SHA-256: b6e05a3e8193a93db505dbf337528fca72e2e41528b1e92b698a3f0683d74289
  • question-first witness SHA-256: caa8693baf0b91acd09a20215d1aa6954ae513fc0b0814f26ac1c8c834b60d67
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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