What Some Puzzling Problems Teach about the Theory of Simulation and the Use of Resampling

Simulation is simpler intellectually than the formulaic method because it does not require that one calculate the number of points in the entire sample space and the number of points in some subset. Instead, one directly samples the ratio. This article presents probabilistic problems that confound even skilled statisticians when attacking the problems deductively, yet are easy to handle correctly, and become clear intuitively, with physical simulation. This analogy demonstrates the usefulness of simulation in the form of resampling methods.