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Abstract
There are numerous economic and sociological and theories addressing the question of how specific aptitudes and talents come to be apportioned among individuals in a population. This paper considers how an arbitrary aptitude or a talent will be distributed among the individuals in a population of a fixed size of it is distributed purely by chance. The main result demonstrates that even if an aptitude or a talent is not objectively measurable, if it is apportioned randomly among the individual in a finite population the specific distribution function can be derived. If the aptitude or talent is empirically measurable, the distribution function derived in this paper can be tested for goodness of fit.