The EJS Uniform Spherical Distribution Model shows how to pick a random point on the surface of a sphere. It shows a distribution generated by (incorrectly) picking points using a uniform random distribution as well as the correct weighted distribution. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting "Open Ejs Model" from the pop-up menu item.
EJS Uniform Spherical Distribution Model
Quelle: Open Source Physics