The nonempty finite sample space is S={3, 4, 5} and the event family is F=𝒫(S). In the displayed order of S, the weights are [16/(17), 1/(17), 0/(17)] and E=∅. Find P(E) exactly as a reduced fraction with positive denominator; do not assume equiprobability.
G001 — The nonempty finite sample space is S={3, 4, 5} and the event family is F=𝒫(S). In the displayed order of S, the weights are [16/(17), 1/(17), 0/(17)] and E=∅. Find P(E) exactly as a reduced fraction with positive denominator; do not assume equiprobability.
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.
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.
Bind weights to ORIGINAL raw S slots;set sorting does not change these associations.Validity needs a positive denominator,all nonnegative weights and the BigInt total equal to the denominator.A model-validity question may legally answerNo,without0/0,sign repair or renormalizing another model.
On the full powerset define every event by its ORIGINAL weighted sum.Nonnegativity,total1 and regrouping disjoint events give finite(and countable,for finite S)additivity.A nonempty E can have mass0.The complement is in the SAME S;do not substitute sorted-slot weights or uniform counts.
S006 · premise_and_result_audit — Reverse-check complete original data,operands and premises;finite checks,conditional reasoning,formal proof and publication authority remain distinct.
S005 · premise_and_result_audit — Recompute Legacy probability ORIGINAL normalized event or complement fraction with exact rational arithmetic, not rounded decimals.
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 probability ORIGINAL ALL numerator weights sum 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
0/1
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.