Symmetry of Sampling Problem Based on Epistemic Uncertainty and Ellsberg Urn

A general sampling problem can be described by an Ellsberg urn, which is a mathematical model that assumes balls are randomly drawn from urn with uncertain numbers of colored balls. This means the essentially intricate simultaneous randomness and epistemic uncertainty, this core discussed in paper. Since practical usually processed environment, solution for equivalent necessary. Suppose contains three unknown (i.e., two-degrees-of-freedom urn), urn. Compared to published papers, paper first constructs chance space two-dimensional uncertainty three-dimensional probability rigorously calculate color distributions those theory, theory. Moreover, it interesting find all cases symmetric such specific situation sample uncertainty.