Sphear of Probabilities
Choose four points on the surface of a sphere. Each point is independently chosen relative to a uniform distribution on the sphere.
What is the probability that the center of the sphere lies inside the tetrahedron whose vertices are at the four points?
The reason this is titled Sphear is that it is a mix of sphere and fear – regular visitors will know of my inability to grasp probabilities, and that Chris will be waiting in the wings to pounce on my weakness!