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A point P is randomly selected from the square region with vertices at (2,2), (2,0), (0,2), (0,0). What is the probability that P is within one unit of the origin? Express your answer as a common fraction in terms of pi.

 Nov 13, 2020
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See the following  :

 

 

Note that this boils down to  finding  the area  of  the quarter circle  with a center at the origin and with a radius of 1 within a square with a side of 2

 

Area of the quarter circle  = pi (1)^2 / 4   =   pi/4

Area of the square  = 2^2   = 4

 

Probability =    area of quarter circle  / area of square  =   (pi/4)  / 4  =   pi / 16 

 

 

cool cool cool

 Nov 13, 2020

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