The course covers the basic principles of the theory of probability and its applications. Topics include combinatorial analysis used in computing probabilities, the axioms of probability, conditional probability and independence of events; discrete and continuous random variables; joint, marginal, and conditional densities, moment generating function; laws of large numbers; Central limit Theorem, binomial, Poisson, gamma, univariate, and bivariate normal distributions, probability spaces, sigma-fields, probability measure and measure theoretic introduction to probability, different modes of convergence