What is the probability that all three will land in the same hemisphere?
Answer below the fold.
100%. As explained at Futility Closet, "Point A, Point B, and the planet’s center determine a plane that cuts the planet in half; Point C must lie on one side or the other of this plane (or directly on the great circle)."
(I suppose someone can argue whether three points on a great circle are in the same hemisphere...)
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