Bertrand’s paradox is a mathematical conundrum that has been addressed by many mathematicians. It deals with the selection of a random chord within a circle and looks for the probabilities that the selected chord is longer than some pre-selected value, usually the length of the sides of the equilateral triangle inscribed on this circle. This work deals with different approaches to the problem and, as a result, leads to different solutions. The existence of several different approaches to solving the problem reveals the importance of precision in posing problems in geometric probability. In this work, we came up with seven different values of the mentioned probability. Some of these values, such as $1\over 4$, $1\over 3$, $1\over 2$, can be obtained using simple arguments. Other more unusual values, such as ${1\over 3} + {\sqrt{3}\over 2\pi}$, are reached by a more in-depth analysis. This work also presents a spatial version of Bertrand’s paradox, where points are chosen on a unit sphere, and the chord is drawn through their projections on the great circle of the sphere.
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