Color distribution of three drawn balls from Ellsberg urn

摘要

Ellsberg urn is a complicated system with uncertainty (the unknown numbers of the colored balls) and randomness (the randomly drawn balls). By supposing that two numbers of colored balls are unknown in an Ellsberg urn, this paper applies uncertainty theory, probability theory and chance theory as rigorous mathematical tools to formulating the color distribution of the drawn balls when three balls are randomly drawn from the urn. Furthermore, an intuitive example is given to illustrate the results obtained by the mathematical method.