Three sharpshooters fire (not simultaneously)
at a rapidly spinning
sphere. If each of them hits the sphere,
what is the probability that all three
shots land in the same hemisphere for
the following two cases: (1) the great
circle dividing the sphere into two
hemispheres can have any orientation
and (2) the great circle dividing
the sphere into two hemispheres
must pass through the sphere’s poles?
Assume each point on the sphere has
an equal chance of being hit.
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