This definition was given by Van Mises.

If a trial is repeated a number of times under essentially homogenous and identical conditions, then the limiting value of the ratio of the number of times the event happens to the number of trials, as the number of trials becomes indefinitely large is called the probability of happening of the event.
It is assumed here that the limit is finite and unique.

Symbolically, if in n trials, an event A happens m times, then the probability ‘p’ of the happening of A is
This definition is an effort to overcome the limitations of the mathematical definition and is a result of the law of statistical regularity. The law of statistical regularity states that if random experiments are repeated a large number of times, even though there is an unpredictable behaviour of
the individual results, the average results of long sequences of random experiments show a visible regularity.
Apparently, the two definitions of probability are different. The first one is the relative frequency of favourable cases to the total number of cases while in the later it is the limit of the relative frequency of the happening of the event.

Limitations of relative frequency approach

1. The condition of an experiment may
not remain the same in long series
of trials

2. The relative frequency may not
attain a unique value inspite of a
large number of trials
-field:
Let S be non-empty class of subsets of  then S is called a -field on  if
(a)   S
(b) For any A  S  Ac  S
(c) S is closed under the formation of
countable unions, i.e.,

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