Probability a Random Triangle Contains the Center of a Circle
Pick three points independently and uniformly at random on the unit circle. They form a triangle $T$.
1. What is the probability that $T$ contains the center of the circle?
2. Give a clean argument using circular orderings and complementary events.
3. Now suppose the three points are drawn i.i.d. uniformly on the circumference of an ellipse instead. Does the answer change? Why or why not?
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