第 28312 題：加權模型的補事件機率

原題與已知條件

非空有限樣本空間 S={-1, 0, 1}，事件族 F=𝒫(S)。依 S 列示順序的權重為 [3/18, 2/18, 13/18]，事件 E={-1, 0, 1}。求精確 P(S∖E)，不可假設等可能。

• G001 — 非空有限樣本空間 S={-1, 0, 1}，事件族 F=𝒫(S)。依 S 列示順序的權重為 [3/18, 2/18, 13/18]，事件 E={-1, 0, 1}。求精確 P(S∖E)，不可假設等可能。

定義與適用範圍

沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。

• mko-probability

逐步推導

source roles = [qf-probability-complement, complement]

derived = [[reduced_same_carrier_complement_fraction_retaining1]]

source roles = [[-1, 0, 1], powerset(S)]

derived = [[-1, 0, 1], 3]

Legacy probability ORIGINAL ALL numerator weights sum := sum(3, 2, 13)

Legacy probability ORIGINAL ALL numerator weights sum = 18

source roles = [[-1, 0, 1], [3, 2, 13], 18]

derived = [[[-1, 3], [0, 2], [1, 13]], 18, 是, 是, 是, 是]

Legacy probability ORIGINAL included outcome-1 running sum0 := sum(0, 3)

Legacy probability ORIGINAL included outcome-1 running sum0 = 3

Legacy probability ORIGINAL included outcome0 running sum1 := sum(3, 2)

Legacy probability ORIGINAL included outcome0 running sum1 = 5

Legacy probability ORIGINAL included outcome1 running sum2 := sum(5, 13)

Legacy probability ORIGINAL included outcome1 running sum2 = 18

Legacy complement ORIGINAL denominator minus event mass := sub(18, 18)

Legacy complement ORIGINAL denominator minus event mass = 0

Legacy probability ORIGINAL normalized event or complement fraction := div(0, 18)

Legacy probability ORIGINAL normalized event or complement fraction = 0

source roles = [[-1, 0, 1], [-1, 0, 1], [[-1, 3], [0, 2], [1, 13]], 18]

derived = [18, [], 0, 0/1]

逐步反向核對

• S010 · premise_and_result_audit — 回查完整來源資料、原操作數及本步條件；有限核對、條件式理由、形式證明與發布資格分開。
• S009 · premise_and_result_audit — 以精確有理數重算 Legacy probability ORIGINAL normalized event or complement fraction，不以小數近似替代。
• S008 · premise_and_result_audit — 以精確有理數重算 Legacy complement ORIGINAL denominator minus event mass，不以小數近似替代。
• S007 · premise_and_result_audit — 以精確有理數重算 Legacy probability ORIGINAL included outcome1 running sum2，不以小數近似替代。
• S006 · premise_and_result_audit — 以精確有理數重算 Legacy probability ORIGINAL included outcome0 running sum1，不以小數近似替代。
• S005 · premise_and_result_audit — 以精確有理數重算 Legacy probability ORIGINAL included outcome-1 running sum0，不以小數近似替代。
• S004 · premise_and_result_audit — 回查完整來源資料、原操作數及本步條件；有限核對、條件式理由、形式證明與發布資格分開。
• S003 · premise_and_result_audit — 以精確有理數重算 Legacy probability ORIGINAL ALL numerator weights sum，不以小數近似替代。
• S002 · premise_and_result_audit — 回查完整來源資料、原操作數及本步條件；有限核對、條件式理由、形式證明與發布資格分開。
• S001 · premise_and_result_audit — 回查完整來源資料、原操作數及本步條件；有限核對、條件式理由、形式證明與發布資格分開。

結論

0/1

依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。

本題覆核與來源綁定

覆核日期：2026-10-26

原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。