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Three friends, Olga, Xin, and Yael, agree to meet in a perfectly circular park. Each friend is dropped off by a different taxi (independently)

 

Three friends, Olga, Xin, and Yael, agree to meet in a perfectly circular park. Each friend is dropped off by a different taxi (independently) at a random point of the park's perimeter. Calculate the probability that all three friends get dropped off in the same semi-circle. Use the geometric method to figure it out: Treat the point where Olga got dropped off as the "origin". If you represent the park's circumference as a line (imagine stretching it out), where could Xin and Yael be dropped off, so that the three friends are in the same semi-circle?

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