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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

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 =  $\dfrac{\pi}{16}$