A black and white colored sphere is given.
We are looking at a random starting point on the sphere below us, which has a certain color. A random rotation can change the color of the spot below us.
What is the probability P that a random rotation of the sphere will change the color of the spot below us from black to white?
Is the following calculation correct:
P = black_surface_fraction * white_surface_fraction
where the "surface fraction" gives the area percentage of the sphere that is black or white?