Due to extensive utilization of intermittent energy sources in recent years, deterministic approaches cannot provide an accurate security assessment for power systems under large uncertainties. Therefore, probabilistic approaches have become crucial for making decisions based on more reliable assessments. In this paper, a new method based on machine learning and proper sampling techniques is proposed to overcome the difficulties of the conventional Monte Carlo approaches used in power system security assessment. The main purpose of the proposed method is to accurately quantify the dynamic security related risk at a forecasted operating condition of a power system utilizing a large number of intermittent energy sources, e.g., wind, which greatly extends the uncertainties in its operation. This is achieved through the proposed method, which captures an accurate probability distribution of the system's dynamic performance associated with both transient and small-signal angle stability. The accuracy of the fitted distribution is attained by adopting a generalized Pareto (GP) distribution for the left-tailed region that includes severe and rare cases using a multilayered perceptron neural network with the Relief feature selection technique, which speeds up the exceedance sample generation process required for the GP distribution. The Latin hypercube sampling technique, which samples the search space evenly, is proposed to create a dataset for training the neural network. To generate the Monte Carlo instances, the Gibbs sampling approach, which considers the correlation between random variables besides its simplicity, is utilized.