4 points on a sphere
Geometry
Level
2
Suppose there is a sphere. If I randomly select 4 points on the sphere, what is the likelyhood of the center of the sphere being contained in the tetrahedron formed by the 4 points?
Answer with a decimal, not a fraction.
The answer is 0.125.
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1 solution
This video https://www.youtube.com/watch?v=OkmNXy7er84 provides a very good discussion of this problem and problem solving in general, and if you haven't seen the channel 3Blue1Brown before, you should definitely check it out. A bit of internet incest: it turns out that this video was how I found out about brilliant.org.