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Conditions required to yield exactly one solution in Bertrand's Paradox
Introduction: Bertrand's Paradox
Given two concentric circles ($S_1$, $S_2$) with radii $R_1=r$ and $R_2=\frac{r}2$, what is the probability, upon choosing a chord $c$ of the circle $S_1$ at random,...
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Expected value of the distance between 2 uniformly distributed points on circle
I have the following problem (related to Bertrand):
Given a circle of radius $a=1$. Choose 2 points randomly on the circle circumference.
Then connect these points using a line with length $b$. ...
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