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 $\pi$.

Lightning
Mar 31, 2018

#1**+2 **

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 * 1^{2 }) / ( 4^{2} )

= pi / 16

hectictar
Mar 31, 2018

#2**+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 = \(\dfrac{\pi}{16}\)

Melody
Mar 31, 2018