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A point $P$ is randomly selected from the square region with vertices at $(\pm 2, \pm 2)$. What is the probability that $P$ is within one unit of the origin? Express your answer as a common fraction in terms of $\pi$.

 Mar 31, 2018
 #1
avatar+7350 
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Here's a graph for reference:  https://www.desmos.com/calculator/nu0suazdzo

 

side length of square  =  4

radius of circle  =  1

 

probability that a point in the square is in the circle

=  area of circle / area of square

=  ( pi * 12 ) / ( 42 )

=   pi / 16

 Mar 31, 2018
 #2
avatar+99232 
+2

A point P is randomly selected from the square region with vertices at \((\pm 2, \pm 2) \). What is the probability that P is within one unit of the origin? Express your answer as a common fraction in terms of pi

 

Area of square = 4*4=16 u^2

Area of circle = \(\pi r^2=\pi*1^2=\pi\;\;units^2\)

 

Prob that the point will be in the circle =  \(\dfrac{\pi}{16}\)

 

 

 Mar 31, 2018

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