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\(\text{A point in space $(x,y,z)$ is randomly selected so that $-1\le x \le 1$,$-1\le y \le 1$,$-1\le z \le 1$. What is the probability that $x^2+y^2+z^2\le 1$? }\)

 Jul 23, 2019
 #1
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I believe that this probability  is just the ratio of the volume of a sphere with a radius of 1 inscribed in  a cube with a side of 2

 

So.....we have that

 

(4/3)pi (1)^3            (4/3) pi          4 pi            pi

__________  =     _______  =   _____  =   ____ ≈    .5236   ≈   52.36 %

    2^3                         8                 24              6

 

 

cool cool cool

 Jul 23, 2019

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