medium Probability
A release-checked medium problem for training Paradoxes, Uniform, Geometric Probability.
A random chord is formed by selecting two uniformly random points, say $X_1$ and $X_2$, on the circumference of the unit circle and connecting a line segment between them. Find the probability that the length of this chord is at least $\sqrt{3}$.
This Probability problem is tagged Paradoxes, Uniform, Geometric Probability. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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