Probability is the possibility that any given event will occur. Empirical probability is regarded as an objective probability, which describes the extent up to which an event has occurred in the past. Hence, it is also called the relative frequency or experimental probability. This makes empirical probability different from others. We get better results from a practical situation, as compared to a theoretical approach.
In mathematical terms, Empirical Probability is defined as the ratio of number of times a particular event occurs to the total number of trials that took place for that expected outcome to occur.
FORMULA FOR AN EMPIRICAL PROBABILITY
Empirical probability depends upon how the event had occurred during the trials. The formula for Empirical probability is given below:
P(E) = Number of times an event occursTotal number of times the experiment is performed (number of trials)
where,
Number of times an event occurs  refers to the number of times a favourable event has occurred
Total number of times the experiment is performed (number of trials) – refers to the total number of times the event was performed
However, it is to be noted that in empirical probability, the experimental conditions may differ from one experiment to the other. This is the reason that an empirical probability is regarded as an estimate of an event from a statistical point of view.
According to a famous mathematician, Thompson, empirical probability is denoted with a prime notation. This is expressed as follows:
P′(A) = n(A)n
where:
There is a particular way to calculate empirical probability. Usually, the empirical probability is based upon the law of large numbers. If you are looking for a precise answer, you need to gather more information and then perform the entire calculation. The larger the volume of information or data, the higher is the accuracy.
ILLUSTRATION ON EMPIRICAL PROBABILITY
Let us look at this simple example that will help you understand empirical probability better.




















Determine the probability of getting tails:
i) Less than 4 times
ii) Equal to 5 times
iii) More than 6 times
ANSWER:
Total number of heads that occurred in this experiment = 2 + 15 + 29 + 57 + 70 + 59 + 20 + 10 + 8 = 270
i) P (occurred tails less than 4)
As per the given table, we could see that = 2 + 15 + 29 + 57 = 103
Thus, P (tails less than 4) = 103/270 = 0.38
ii) P (occurred tails equal to 5).
From given table, the required number of cases = 59
Therefore, P (tails equal to 5) = 59/270 = 0.22
iii) P (more than 6 tails)
Total number of cases = 18
So, P (tails more than 6) = 18/270 = 0.07