Empirical probability refers to the likelihood of an event occurring, determined through observed data rather than theoretical calculations.

This type of probability, also known as experimental probability, is computed by taking the ratio of the number of times an event occurs to the total number of trials or observations. For instance, if a coin is flipped $100$ times and results in heads $60$ times, the empirical probability of the coin landing on heads can be expressed as

Empirical probability is particularly valuable in situations where calculating theoretical probabilities is challenging or unfeasible. For example, in a medical study, researchers might determine the empirical probability of a treatment’s effectiveness by dividing the number of patients who showed a positive response to the treatment by the total number of patients who received it.

However, empirical probability has its limitations. It is derived from a finite set of data, which may not accurately represent the true probability of an event. As additional data is gathered, the empirical probability may shift. Furthermore, factors such as sample size and selection bias can significantly influence the results.

In summary, empirical probability serves as a practical method for estimating probabilities based on observed data. Nonetheless, it is crucial to remain aware of its limitations and potential sources of error when applying this approach to real-world situations.