Read the following question and provide a solution: Four points are chosen at random on the interior surface of a sphere. What is the probability that the center of the sphere lies inside the tetrahedron whose vertices are formed from the four random points? Be sure to provide mathematical evidence that adequately shows the process you took to arrive at your solution.

The image below has been attached to provide a mental image of the aforementioned sphere and is to be used in solving this problem.

NOTE: [Incorrect/irrelevant/spam answers will be reported!]