AMC8 2009

AMC8 2009 · Q10

AMC8 2009 · Q10. It mainly tests Probability (basic), Area & perimeter.

On a checkerboard composed of 64 unit squares, what is the probability that a randomly chosen unit square does not touch the outer edge of the board?

在一个由64个单位方格组成的棋盘上，随机选择的单位方格不接触棋盘外边缘的概率是多少？

(A) \frac{1}{16} \frac{1}{16}

(B) \frac{7}{16} \frac{7}{16}

(D) \frac{9}{16} \frac{9}{16}

(E) \frac{49}{64} \frac{49}{64}

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): The checkerboard has 64 unit squares. There are $2\cdot 8 + 2\cdot 6 = 28$ unit squares on the outer edge, and $64 - 28 = 36$ unit squares in the interior. Therefore the probability of choosing a unit square that does not touch the outer edge is $\frac{36}{64}=\frac{18}{32}=\frac{9}{16}$.

答案（D）：棋盘有 64 个单位小正方形。外边缘上有 $2\cdot 8 + 2\cdot 6 = 28$ 个单位小正方形，内部有 $64 - 28 = 36$ 个单位小正方形。因此，选到一个不接触外边缘的单位小正方形的概率为 $\frac{36}{64}=\frac{18}{32}=\frac{9}{16}$。

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