Theoritical vs Experimental Probability

One of the classifications of probabilities is into experimental probability and theoretical probability. If actual experiments are carried out and probability numbers derived are from the results of actual experiments, the probability is called the experimental probability . Instead, if you derive the probability using mathematical ways without actually carrying out the experiment in reality, we call it Theoretical Probability. We try to derive mathematically what would be the scenario if the experiments were performed in a controlled environment in an ideal scenario (which is practically impossible to achieve). The values from experimental probability do not exactly match theoretical probability because theoretical probability is based on ideal case scenario whereas experimental probability is based on actual experiments. When you do actual experiments a lot of factors come into picture. For eg flipping a coin according to theoretical probability should ideally give you head once and tail next time. Whereas when you actually flip a coin you may end up getting two heads both the times and hence is different from your theoretical probability. A lot of factors like air speed at that time, no of rotations of coin, fairness of coin all result in experimental probability coming out different from theoretical probability. It is only when we carry out the experiment a very high no of times say close to infinity the theoretical and experimental probability tend to converge.