Question 28528: Finite Point Probability of a Repeated Value

Original question and givens

The nonempty finite sample space is S={0, 1, 2, 3}, with event family F=𝒫(S). The total function X:S→R has table {(0, -3), (1, -3), (2, 4), (3, 1001)}. In the displayed order of S, the nonnegative probability weights are [1/(8), 4/(8), 3/(8), 0/(8)], summing exactly to one. Find P(X=1001) exactly as a reduced fraction p/q with positive denominator.

• G001 — The nonempty finite sample space is S={0, 1, 2, 3}, with event family F=𝒫(S). The total function X:S→R has table {(0, -3), (1, -3), (2, 4), (3, 1001)}. In the displayed order of S, the nonnegative probability weights are [1/(8), 4/(8), 3/(8), 0/(8)], summing exactly to one. Find P(X=1001) exactly as a reduced fraction p/q 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.

• mko-random-variable

Step-by-step derivation

source roles = [qf-random-variable-point-mass, rv_point_mass]

derived = [probability_of_complete_value_fibre]

source roles = [[0, 1, 2, 3], powerset(S), [-3, -3, 4, 1001]]

derived = [[[0, -3], [1, -3], [2, 4], [3, 1001]]]

RV ORIGINAL all aligned numerator weights := sum(1, 4, 3, 0)

RV ORIGINAL all aligned numerator weights = 8

source roles = [[[0, -3, 1], [1, -3, 4], [2, 4, 3], [3, 1001, 0]], 8, 1001]

derived = [8, [[0, -3, 1, No], [1, -3, 4, No], [2, 4, 3, No], [3, 1001, 0, Yes]]]

RV ORIGINAL matching slot3 outcome3 mass := sum(0, 0)

RV ORIGINAL matching slot3 outcome3 mass = 0

RV ORIGINAL complete fibre mass over denominator := div(0, 8)

RV ORIGINAL complete fibre mass over denominator = 0

source roles = [[[0, -3, 1], [1, -3, 4], [2, 4, 3], [3, 1001, 0]], 1001, 0, 8]

derived = [0/1]

Reverse checks

• S007 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance.
• S006 · premise_and_result_audit — Recompute RV ORIGINAL complete fibre mass over denominator with exact rational arithmetic, not rounded decimals.
• S005 · premise_and_result_audit — Recompute RV ORIGINAL matching slot3 outcome3 mass with exact rational arithmetic, not rounded decimals.
• S004 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance.
• S003 · premise_and_result_audit — Recompute RV ORIGINAL all aligned numerator weights with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance.
• S001 · premise_and_result_audit — Reverse-check EACH original datum and premise,retaining indices,signs and strict/non-strict boundaries.A correct final answer cannot replace the derivation obligations.This is candidate teaching/exact checking,not formal proof or publication clearance.

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.