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 + y + z <= 0?

(0,0,0) is the centre of this space. It is a sphere of radius 1.

So it seems to me that that P(x+y+z<=0) = 0.5 That is just a guess. I can't claim to be sure.