In this study, a generalized family of discrete probability distributions is discussed. I have derived a general form of probability mass function (pmf) for the family of discrete probability distributions (FDPD) which belongs all standard discrete probability distributions. From the derived single general pmf any one can easily find the pmf for all the members of FDPD by only suitable choices of some factors given in Table 5.1. Therefore it might be regarded as a convenient, time saving, simplex and generalized device in the theory of probability. Particular cases for standard discrete probability distributions are also illustrated. Further moment generating function and hence some moments, mean and variance of the FDPD discussed as its property.