The main aim of this study is probabilistic computer simulation of the effective physical parameters of fluids containing nanoparticles. A deterministic model following the rule of mixtures and some semi-empirical formulas are employed to calculate effective density, heat conductivity, heat capacity, as well as viscosity for the given nanofluid. This models is randomized here using the Monte-Carlo simulation apparatus for estimation of the Shannon entropy of all these physical parameters, which is the crucial novelty of this study. The volume fraction of the nanoparticles is assumed for this purpose as the Gaussian uncertainty source with the given first two moments. The basic probabilistic characteristics of the nanofluids' homogenized parameters have also been determined here for some validation of Shannon entropy variations in addition to the statistical disorder of the nanoparticle fraction. These research findings contribute to advancing nanofluidic and microfluidic research, offering robust tools for uncertainty analysis and enhancing the reliability of physical parameter predictions in applications requiring high numerical and/or experimental precision.