AMC 8 2009 Problem 10

AMC8 2009 年第 10 题

概率★★☆☆☆

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?

在由 64 个单位正方形组成的棋盘上随机选择一个单位正方形，那么此单位正方形不接触棋盘外缘的概率是多少？

A. $\displaystyle \frac{1}{16}$
B. $\displaystyle \frac{7}{16}$
C. $\displaystyle \frac{1}2$
D. $\displaystyle \frac{9}{16}$
E. $\displaystyle \frac{49}{64}$

正确答案 · Correct Answer

解析 · Solution

Solution 1

There are

8^2=64

total squares. There are (8-1)(4)=28 unit squares on the perimeter and therefore 64-28=36 NOT on the perimeter. The probability of choosing one of those squares is

\displaystyle \frac{36}{64} = \frac{9}{16}

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