Find the probability that three points are chosen on a circle lies on the same semi-circle.
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They are separated by an angle between 0∘ and 180∘ with uniform probability. If the first two points are the same, then the third point must lie on the same semicircle as the first two (probability 1). ... The probability decreases linearly from 1 to 1/2 as the separation of the points goes from 0∘ to 180∘.
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