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Question 28355: Event Probability with Explicit Equiprobability

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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R0055-28355 · q-20261003-r07-probability-0005

Original question and givens

The nonempty finite sample space is S={-8, -7, -6, -5, -4, -3} and the event family is F=𝒫(S). All elementary outcomes are explicitly equiprobable. For E={-8, -6, -4}, find P(E) exactly as a reduced fraction with positive denominator.

  • G001 — The nonempty finite sample space is S={-8, -7, -6, -5, -4, -3} and the event family is F=𝒫(S). All elementary outcomes are explicitly equiprobable. For E={-8, -6, -4}, find P(E) exactly as a reduced fraction with positive denominator.

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-probability-uniform-event, uniform_event]

After

derived = [[reduced_probability_fraction_retaining_integer_denominator1]]

Conditions: none

List this scalar/label/set/point answer role or mode-specific ordered fields,not an imposed universal tuple.Retain legacy domain/underscore operation and integer fractions with/1;original bilingual snapshots stay unchanged.

Step identifiers and dependencies

Rule: source_answer_roles_or_ordered_fields_without_JS · Uses: G001

S002 · implies

Before

source roles = [[-8, -7, -6, -5, -4, -3], powerset(S)]

After

derived = [[-8, -7, -6, -5, -4, -3], 6]

Conditions: none

S is a nonempty set of at most100 distinct SAFE integers and F is explicitly the FULL powerset,not an event family inferred from one event.

Step identifiers and dependencies

Rule: Legacy_probability_NONEMPTY_S_FULLpowerset_exact_declared_event_family · Uses: G001, S001

S003 · calculation

Before

Legacy uniform ORIGINAL event count over carrier count := div(3, 6)

After

Legacy uniform ORIGINAL event count over carrier count = 1/2

Conditions: none

Substitute original roles exactly,without floating approximation or changed operands;extra teaching identities add no source-domain restrictions.

Step identifiers and dependencies

Rule: exact_rational_arithmetic · Uses: G001, S002

S004 · implies

Before

source roles = [[-8, -7, -6, -5, -4, -3], [-8, -6, -4], Yes]

After

derived = [1/2]

Conditions: none

Only the exactBoolean true equiprobability premise permits |E|/|S|.An empty event gives0/1,the whole space1/1,and integer fractions retain/1.

Step identifiers and dependencies

Rule: Legacy_uniform_requires_EXACT_equiprobability_not_cardinality_guess · Uses: G001, S003

Reverse checks

  • S004 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.
  • S003 · premise_and_result_audit — Recompute Legacy uniform ORIGINAL event count over carrier count with exact rational arithmetic, not rounded decimals.
  • S002 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.
  • S001 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.

Result

1/2

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: f4c72e78a6d0bd1311a723ad7f262502e3b4ce7fdb70afad80917d2ad39aaa3d
  • candidate record SHA-256: ad92d9b3c37f20d892e00c4d111575611fc488a7ea9cc64877d048a82a57c9a6
  • semantic review receipt SHA-256: 6af367dae24a584f3596525c4953bbc2115343efd68cc9083693eb5c1ef2e683
  • question-first witness SHA-256: 611eb69f3716404b968296a8b0d7d8c61b5ca18129d406f1ff9c7c11e10ffb4e
  • Lean: NOT_RUN · human review: NOT_PERFORMED
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