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Openai/695dfc16-b2ac-8005-980b-b86d96450929
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=== Assistant: 我們先把規則完整拆清楚,再逐一判斷(1)~(5)。 === 我們先把規則完整拆清楚,再逐一判斷(1)~(5)。 ==== 抽到的號碼: ==== n∈{0,1,2,3,4,5,6,7,8,9},等機率n \in \{0,1,2,3,4,5,6,7,8,9\},\quad \text{等機率}n∈{0,1,2,3,4,5,6,7,8,9},等機率 神的處理方式: x=10n/10,N=⌊x⌋x = 10^{n/10},\quad N=\lfloor x \rfloorx=10n/10,N=⌊x⌋ 先列出每個 nnn 對應的 NNN: | | | | | | --- | --- | --- | --- | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 整理成葉序分類: * 互生(N=1):n = 0,1,2,3 * 對生(N=2):n = 4 * 輪生(N ≥ 3):n = 5,6,7,8,9 ==== ### ==== 互生對應 n = 0,1,2,3,共 4 個號碼 P=410=40%P=\frac{4}{10}=40\%P=104=40% ❌ 錯誤(不是 30%,是 40%) ===== 先解方程式: ===== (p−5)3−4(p−5)=0(p-5)^3-4(p-5)=0(p−5)3−4(p−5)=0 令 q=p−5q=p-5q=p−5: q(q2−4)=0⇒q=0,±2q(q^2-4)=0 \Rightarrow q=0,\pm2q(q2−4)=0⇒q=0,±2 p=5,7,3p=5,7,3p=5,7,3 檢查這些號碼的葉序: * p=3 → N=1(互生) * p=5 → N=3(輪生) * p=7 → N=5(輪生) 沒有任何一個得到 N=2(對生) ❌ 錯誤 ===== 對生 ⇔ N=2 ===== 由表格可知 只有 n=4 會得到 N=2 ✔ 正確 ===== 互生 ⇒ n ∈ {0,1,2,3} ===== 期望值: E=0+1+2+34=1.5E=\frac{0+1+2+3}{4}=1.5E=40+1+2+3=1.5 ✔ 正確 ===== 實際對應: ===== * n=5 → N=3 ✔ * n=6 → N=3 ❌(不是 4) * n=7 → N=5 ✔ 沒有任何 n 對應到 N=4 ❌ 錯誤 ==== 正確選項是: ==== (3)、(4)\boxed{(3)、(4)}(3)、(4) 如果你要,我也可以幫你把這題整理成 👉 考試型「一眼判斷表」 👉 或改成 陷阱題解析版(為什麼直覺會選錯)
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