In this compilation, the authors first consider applying the Monte Carlo method to the general form of the heat equation that is used for analyzing conduction heat transfer. The Monte Carlo method is then extended to some convection heat transfer applications by representing the probabilistic interpretation of the energy equation to obtain the temperature profile. Following this, Monte Carlo Methods: History and Applications discusses the Monte Carlo methods needed for the estimation of the mean glandular dose in both digital mammography and digital breast tomosynthesis. Various breast anatomies are considered. The gradual development of the Monte Carlo method for solving problems of mathematical chemistry is considered. A comparison of various quantitative structure -- property/activity relationships based on the Monte Carlo method is also presented. Lastly, the Monte Carlo technique is used to characterize the statistical distributions of received measurements in an electric energy power system, as well as to quantify the correlations among these variables. To check the numerical accuracy of the results, the point estimate algorithm is employed.