Statistical Definition of Probability
In the classical definition of probability, the evaluation of probability was done in some simple cases making use of our intuitive notion of chance. However, in more complex situations, the evaluation of probability will have to be based on observational or experimental evidence.
The estimate of probability of a specified outcome based on a series of independent trials is given by
Probability = (The number of times the outcome occurred)/(Total number of trials)
Sometimes, this probability is referred to as posteriori probability, that is, after the event.
Remarks: Since in the relative frequency approach, the probability is obtained objectively by repetitive empirical observations, it is known as ‘Empirical Probability’ Only after repeated trials, it can be established that the chance of head in a toss of a coin is ½. J.E. Kerrich conducted coin tossing experiment with 10 sets of 1,000 tosses each during his confinement in World War II. The numbers of heads found by him were: 502, 511, 497, 529, 504, 476, 507, 520, 504, 529.
This gives the probability of getting a head in a toss of a coin as
= 5079/10,000 = 0.5079= ½ .
Thus, the empirical probability approaches the classical probability as the number of trials becomes indefinitely large.
Example: if we want to know the probability of success of a surgical procedure, a review of past experience of this surgical procedure under similar conditions will provide the data for estimating probability. The longer the series we have, the closer the estimate would be to the true value.
