Elementary random events possibly favorable to a random event are defined as those elementary random events for which we are not able to prove or deduce, within the limited framework of a decision procedure being at our disposal, that they are not favorable to the random event in question. Under some conditions, probabilities of the sets of possibly favorable elementary random events induce uniquely a possibilistic measure on the system of all subsets of the universe of elementary random events under consideration. Moreover, each possibilistic measure defined on this power-set can be obtained, or at least approximated to the degree of precision a priori given, in this way. Some results concerning the combinations of decision systems and decision systems induced by random variables are introduced and proved.