91Ó°ÊÓ

Consider an experiment whose sample space consists of a countably infinite number of points.

Let us consider the hypothesis that all points are equally likely.

Let $n$be the number of points and $p$the nonzero probability of each point.

Hence, $np=1.$However, as $n$is infinite, so must be localid="1649303133978" $np,$which therefore cannot equal$1$. It is thus impossible that all points have equal probability.

To guarantee that $np=1$it is necessary that $n$be finite. In other words, there must be a finite number of points with a positive probability of occurring, excluding from the sample space all other points, the probability of which being zero. It is impossible for an infinitely large number of points to have a positive probability of occurring.