+0  
 
0
58
1
avatar

A point P is randomly selected from the square region with vertices at $(\pm 1, \pm 1)$. 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 27, 2021
 #1
avatar+22553 
+1

The probability of being within one unit of the origin is the area within a circle centered at the origin with

a radius of 1 divided by the area of a square with side lengths of 2.

 

The area of the circle is:  pi · r2  =  pi · 12  =  pi.

 

The area of the square is  2 · 2  =  4

 

The probability is  pi / 4

 Nov 27, 2021

12 Online Users