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