ABSTRACT
In most issues where chance plays a part, things seem to behave rather
erratically if one looks only at a few instances. On the other hand, this
type of behaviour seems to 'smooth out' in the long run. In other words,
as the number of observed instances - or trials or experiments - increases,
a more and more orderly pattern seems to ensue and certain regularities
become clearer and clearer. This is what happens, for example, when we
toss a coin; after 10 tosses we would not be surprised to have, say, eight
heads and two tails but we would surely be if we got 800 heads and 200
tails after 1000 tosses. In fact, in this case we would seriously suspect that
the coin is biased. This state of affair would be intriguing but not partic-
ularly interesting if it applied only to coins and dice. As a matter of fact,
however, a large number of experiences in many fields of human activities -
from birth and death rates to accidents, from measurements in science and
technology to the occurrence of hurricanes or earthquakes, just to name a
few - behave in a similar manner when measured, tabulated and/or assigned
numerical values. The appearance of long-term regularities as the number
of trials increases has been known for centuries and goes under the name
of 'law of large numbers'. The great achievement of probability theory is in
having established the general conditions under which these regularities can
and do occur.
