The circle is symmetric, so place one point anywhere and ask whether the other three land in the same semicircle. Each of those 3 points independently has a 1/21/21/2 chance of landing in that half, so the probability should be (1/2)3=1/8=12.5%(1/2)^3 = 1/8 = 12.5\%(1/2)3=1/8=12.5%.
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