The scope of the classical definition was found to be very limited as it failed to determine the probabilities of certain events in the following circumstances :
In view of the above shortcomings of the classical definition, an attempt was made to establish a correspondence between relative frequency and the probability of an event when the total number of trials become su1fficiently large.
Definition (R. Von Mises)
If an experiment is repeated n times, under essentially the identical conditions and, if, out of these trials, an event A occurs m times, then the probability that
This definition of probability is also termed as the empirical definition because the probability of an event is obtained by actual experimentation.
Although, it is seldom possible to obtain the limit of the relative frequency, the ratio m/n can be regarded as a good approximation of the probability of an event for large values of n.
This definition also suffers from the following shortcomings :
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