The primary objective in sampling is to acquire the smallest sample as a reliable estimate of a particle population. This study aims to assess the threshold (minimum) sample sizes for reliable estimation of particle size distributions. For that purpose, samples were simulated from particle populations artificially generated from the Gates-Gaudin-Schumann model. Then, two-sample Kolmogorov-Smirnov and Chi-Square Goodness-of-Fit tests were implemented between the number-weighted size distributions of samples and their parent populations. Results suggest that continuous size distributions can be estimated with at least 36-40% of the number of population particles. Corresponding masses to estimate continuous distributions varies between 34% and 68% population mass, where smaller populations may require larger samples. Results indicate that probabilistic sampling may be insufficient to estimate the discrete number-weighted size distributions. Probabilistic sampling seems insufficient to estimate the mass-weighted size distribution of widely sized population particles. Estimating mass-weighted distributions requires larger samples than their number-weighted equivalents. Mass-weighted size distributions of samples better fit at the finest or the coarsest size ranges than the mid-size range of their population. If a population is large, the percent population mass taken as a sample is nearly equal to the percent number of population particles.