A Tilted Cap
A point (x, y, z) is chosen uniformly at random on the surface of the unit sphere x² + y² + z² = 1. What is the probability that x + y + z > 1? Give an exact closed form, or a decimal rounded to 4 places.
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Source: Uses Archimedes' hat-box theorem; problem in wide circulation in this form. Statement written for AxiomIQ.