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Three points are selected at random on a sphere's surface. What is the probability that they all lie in same hemisphere?

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Three points are selected at random on a sphere's surface. What is the probability that they all lie in the same hemisphere?
Assume that the great circle, bordering a hemisphere, is part of the hemisphere.

posted Jul 27, 2016 by anonymous

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2 Answers

+1 vote
 
Best answer

No matter how we place the points on a sphere it will without any doubt fall in one of the infinite possible hemispheres that can be chosen.

So the asked probability is 1 ie., 100%.

answer Aug 9, 2016 by Tejas Naik
+2 votes

In space, the three points define a plane cutting the sphere in two pieces. The smaller of these two spherical caps is always contained in half of a sphere: a hemisphere.
Thus the answer is: 100% probable.

answer Aug 9, 2016 by anonymous



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