Ellsberg urn problems with multiple degrees of freedom

An Ellsberg urn is filled with n balls of m different colors and each ball is marked in only one color. However, the number of balls of each color is unknown, which should be regarded as uncertain variable. Moreover, since we randomly draw a ball from the urn, Ellsberg urn problems are a mixture of uncertainty and randomness. In order to deal with such problems, we can employ probability theory, uncertainty theory, and chance theory. Until now only the case m = 3 has been studied. This paper is aimed at studying more general cases where m > 3. It is concluded that the chance of drawing a ball of one color is equal to that of drawing a ball of another color.