Statistical Probability

Statistical probability is one of three main intrepretations of the concept of probability (classical probablity and subjective probability are the other two). In statistical probability, also referred to as relative frequency probability, the probability of an event is considered to be the relative frequency with which an event occurs after repeating an experiment a large number of times. Relative frequency probability is well-suited to apply to problems in the natural and social sciences and in many other fields.

Suppose that a fair coin were flipped a large number of times. By the law of large numbers, we would expect the that both the relative frequency of heads and the relative frequency of tails would approach ½ as the more and more flips were done. So, we would likely conclude that the probability of a head is around ½ based on the results of these trials.

While statistical probability can be used to model a wide range of phenomena, it too has its limitations. Taking the example of flipping a fair coin, our trial will almost certainly yield a relative frequency for heads around ½. However, this value will be slightly different every time we flip a coin a lot of times, even though the real probability of flipping the coin never changes. Getting the exact probability would require that we perform an infinite number of trials, which we can't do.