Considering probability theory in which the semifield of positive real numbers is replaced by the idempotent semifield of real numbers (union infinity) endowed with the min and plus laws leads to a new formalism for optimization. Probability measures correspond to minimums of functions that we call cost measures, whereas random variables correspond to constraints on these optimization problems that we call decision variables. We review in this context basic notions of probability theory -- random variables, convergence of random variables, characteristic functions,, $L^p$ norms. Whenever it is possible, results and definitions are stated in a general idempotent semiring