Difference between revisions of "2009 AMC 8 Problems/Problem 10"
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fill((5,7)--(6,7)--(6,8)--(5,8)--cycle,black); | fill((5,7)--(6,7)--(6,8)--(5,8)--cycle,black); | ||
fill((7,7)--(8,7)--(8,8)--(7,8)--cycle,black);</asy> | fill((7,7)--(8,7)--(8,8)--(7,8)--cycle,black);</asy> | ||
− | <math> \textbf{(A)}\frac{1}{16}\qquad\textbf{(B)}\frac{7}{16}\qquad\textbf{(C)}\ | + | |
+ | <math> \textbf{(A)}\ \frac{1}{16}\qquad\textbf{(B)}\ \frac{7}{16}\qquad\textbf{(C)}\ \frac{1}2\qquad\textbf{(D)}\ \frac{9}{16}\qquad\textbf{(E)}\ \frac{49}{64} </math> | ||
+ | |||
+ | ==Solution== | ||
+ | There are <math>8^2=64</math> total squares. There are <math>(8-1)(4)=28</math> unit squares on the perimeter and therefore <math>64-28=36</math> NOT on the perimeter. The probability of choosing one of those squares is <math>\frac{36}{64} = \boxed{\textbf{(D)}\ \frac{9}{16}}</math>. | ||
==See Also== | ==See Also== | ||
{{AMC8 box|year=2009|num-b=9|num-a=11}} | {{AMC8 box|year=2009|num-b=9|num-a=11}} |
Revision as of 16:39, 25 December 2012
Problem
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?
Solution
There are total squares. There are unit squares on the perimeter and therefore NOT on the perimeter. The probability of choosing one of those squares is .
See Also
2009 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |