Paradoxes have played an important role in the development of mathematics, as they brought about clarification of basic concepts and the introduction of new approaches. Probability theory offers a large variety of Paradoxes. Some of them are (nowadays) interesting mainly from a historical point of view, as the theory has already been adapted to resolve them. Others actually hide common misconceptions in a very subtle and tricky way. Introducing Paradoxes in class carries potential danger: it may result in a feeling of insecurity when the conflict between the mathematical solution and the intuition (or between two seemingly correct mathematical solutions) seems unresolvable. On the other hand, properly introduced, Paradoxes can play a very useful role in the classroom as they serve as leverage to fruitful discussions, and provoke deeper thinking about the (not always intuitive) probabilistic ideas.
The CAUSE Research Group is supported in part by a member initiative grant from the American Statistical Association’s Section on Statistics and Data Science Education