3 ms·

Another interesting paradox in probability is Bertrand’s Paradox[1]. Given an equilateral triangle inscribed in a circle, what is the probability that chord of

• mamon 11y ago
  For me the most messy part is being allowed to rotate the triangle to match it to one of the described cases. Normally, if you assume triangle does not move, and then draw a random chord, then depending on relative position of the chord and triangle you use one of three methods described by Bertrand to judge whether it is longer or shorter than triangle side. Then you need a way to count probability of each of those cases to happen and then count the weighted average of all three "paradoxical" cases. EDIT: in fact I would just bet on Method 3 as a correct solution, because it is the most general: it does not require rotating the triange. If you are rotating the triangle then you are in fact changing problem definition during solving it, which leads to some hidden assumptions (i.e. Method 2 is only good for chords which are parallel to one side of triangle, and Method 1 is only good for chords that do not cross with triangle sides)
  • kgwgk 11y ago
    Actually, as the wikipedia entry mentions, one can argue that Method 2 is the correct one: it is the only one respecting reasonable translation and scale invariance constraints.