Bertrand's Paradox

Bertrand's Paradox arises in probability theory while considering random events. It illustrates that the way we define randomness can lead to different probabilities for the same situation. For example, if you randomly pick a chord in a circle, different methods of defining "random" can result in different chances of that chord being longer than the circle's radius. This paradox highlights the importance of the underlying assumptions in probability calculations and shows that seemingly simple problems can have multiple valid answers depending on how they are framed.