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In evaluating the number of technological civilizations N in the Galaxythrough the Drake formula, emphasis is mostly put on the astrophysical andbiotechnological factors describing the emergence of a civilization and muchless on its the lifetime, which is intimately related to its demise. It isargued here that this factor is in fact the most important regarding thepractical implications of the Drake formula, because it determines the maximalextent of the "sphere of influence" of any technological civilization. TheFermi paradox is studied in the terms of a simplified version of the Drakeformula, through Monte Carlo simulations of N civilizations expanding in theGalaxy during their space faring lifetime L. In the framework of that scheme,the probability of "direct contact" is determined as the fraction of theGalactic volume occupied collectively by the "spheres of influence" of Ncivilizations. The results of the analysis are used to determine regions in theparameter space where the Fermi paradox holds. It is argued that in a largeregion of the diagram the corresponding parameters suggest rather a "weak"Fermi paradox. Future research may reveal whether a "strong" paradox holds insome part of the parameter space. Finally, it is argued that the value of N isnot bound by N=1 from below, contrary to what is usually assumed, but it mayhave a statistical interpretation.

A probabilistic analysis of the Fermi paradox in terms of the Drake formula: the role of the L factor