  We consider an ergodic process on finitely many states, with positive
entropy. Our first main result asserts that the distribution function of the
normalized waiting time for the first visit to a small (i.e., over a long
block) cylinder set $B$ is, for majority of such cylinders and up to epsilon,
dominated by the exponential distribution function $1-e^{-t}$. That is, the
occurrences of so understood "rare event" $B$ along the time axis can appear
either with gap sizes of nearly exponential distribution (like in the
independent Bernoulli process), or they "attract" each-other. Our second main
result states that a {\it typical} ergodic process of positive entropy has the
following property: the distribution functions of the normalized hitting times
for the majority of cylinders $B$ of lengths $n'$ converge to zero along a \sq\
$n'$ whose upper density is 1. The occurrences of such a cylinder $B$ "strongly
attract", i.e., they appear in "series" of many frequent repetitions separated
by huge gaps of nearly complete absence.
  These results, when properly and carefully interpreted, shed some new light,
in purely statistical terms, independently from physics, on a century old (and
so far rather avoided by serious science) common-sense phenomenon known as {\it
the law of series}, asserting that rare events in reality, once occurred, have
a mysterious tendency for untimely repetitions.
