AMC 8 2026 Problem 21

AMC8 2026 年第 21

概率★★★☆☆
Charlotte the spider is walking along a web shaped like a 5-pointed star, shown in the figure below. The web has 5 outer points and 5 inner points. Each time Charlotte reaches a point, she randomly chooses a neighboring point and moves to that point. Charlotte starts at one of the outer points and makes 3 moves (re-visiting points is allowed). What is the probability she is now at one of the outer points of the star?
是一只蜘蛛,她在一张形如五角星的网上爬行(如下图所示)。这张网有 5 个外顶点和 5 个内顶点。每次 Charlotte 到达一个顶点时,会随机选择一个相邻顶点并移动过去(允许重复访问)。她从一个外顶点出发,共移动 3 次。此时她位于外顶点的概率是多少?
AMC 8 2026 Problem 21 figure
  1. A.15\displaystyle \frac{1}{5}
  2. B.14\displaystyle \frac{1}{4}
  3. C.25\displaystyle \frac{2}{5}
  4. D.12\displaystyle \frac{1}{2}
  5. E.35\displaystyle \frac{3}{5}

正确答案 · Correct Answer

B

解析 · Solution

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