### Instruction: 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 $x^2+y^2+z^2\le 1$?### Response: I need to find the volume of the region inside the cube $[-1,1]^3$ that satisfies $x^2+y^2+z^2\le 1$.
This region is a sphere with radius 1 centered at the origin, so its volume is $\frac{4}{3}\pi r^3=\frac{4}{3}\pi$.
The volume of the cube is $2^3=8$, so the probability that a random point in the cube is also in the sphere is $\frac{\text{volume of sphere}}{\text{volume of cube}}=\frac{\frac{4}{3}\pi}{8}=\frac{\pi}{6}$.