Binary stars are gravitationally bound stellar systems where the evolution of each component can significantly influence the evolution of its companion and the system as a whole. In certain cases, the evolution of these systems can lead to the formation of a red giant-white dwarf system, which may exhibit symbiotic characteristics. The primary goal of this work is to contribute in a statistical way to the estimation of the symbiotic system (SySt) population in the Milky Way and in the dwarf galaxies of the Local Group (LG). Additionally, we aim to infer the maximum contribution of SySt to Type Ia supernova (SN Ia) events. Given the significant discrepancies in previous estimates, we propose two distinct approaches to constrain the expected SySt population: one empirical and another theoretical. These approaches are designed to provide a robust estimation of the SySt population. For the Milky Way, we utilized position and velocity data of known SySts to determine their distribution. Based on these properties, we constrained the lower limit for the Galactic SySt population in the range of 800-4100. Our theoretical approach, which relies on the properties of zero-age main-sequence binaries and known binary evolutionary paths, suggests a SySt population of (53+/-6)x10^3^SySt in the Galaxy. The statistical SySt populations for LG dwarf galaxies are one to four orders of magnitude lower, primarily dependent on the galaxies' bolometric luminosity and, to a lesser extent, their binary fraction and metallicity. In this work, the contribution of the single-degenerate channel of SNe Ia from symbiotic progenitors is estimated to be of the order of 1% for the Galaxy.