1.2.2 Empirical Probability
The dictionary meaning of “Empirical” is based on observation or experience. Empirical probability also referred to as experimental probability, centers on real-world experiments and observations. Empirical probability is rooted in the notion that the probability of an event is based on the frequency of that event's occurrence in past experiments.
Empirical probability is determined by counting the number of times an
event has occurred (
) and then dividing it by the total number of trials (
) of an experiment. For an event 
, it can be denoted by the notation:
The empirical probability becomes a more accurate approximation of the true probability as the number of trials in an experiment increases.
Example 1.4. Let's examine the “coin-flipping” experiment through the lens of empirical
probability. Consider a fair coin that was flipped three times (), with “heads” appearing zero times (), as illustrated in Fig 1.2.
Since none of the previous trials yielded “heads”,…