The discussion explores the concept of probability using concentric circles to illustrate how different coordinate systems can yield varying probabilities for the same scenario. When selecting a point randomly in a larger circle, the probability of it falling within a smaller circle can be calculated as 1/4 using Cartesian coordinates. However, when polar coordinates are applied, the probability changes to 1/2 due to the uniform distribution in angle and the squared radial distance. This highlights the importance of the chosen coordinate system in probability calculations. The findings emphasize that the interpretation of probability can vary significantly based on the method used for selection.