Based on the connection between an king model with fourspin interactions and a four-site correlated percolation model, we define cluster-size distributions and the most probable cluster-size distribution for the system. The sum over subgraphs in the correlated percolation model may be written as sum over all possible cluster-size distributions. We find that in the calculation of the free energy and the physical quantity we need only to retain the term of the most probable cluster-size distribution. This result confirms our hypothesis on the most probable cluster-size distribution (H-MPCSD) for interacting systems.