darts anyone, page-22

It a quantitative riddle, abstract thinking is required.

A very similar question to the original posted, without any ambiguity (eeek) is:

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What is the probability that 4 randomly selected points on a sphere are in the same hemisphere?

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Notes:

Hemisphere means half the sphere, through the center. An infinite number of hemispheres can be chosen. So not necessarily north-south

I have an answer and a valid solution based on geometrical arguments. This problem is quite hard..... Well hard for me anyway :-).

My solution requires no math calculations, but a solid understanding of spherical geometry and Cartesian coordinates (i.e. x,y,z axis) are required.