# Probability Theory

## Empirical Probability

The empirical approach to determining probabilities relies on data from actual experiments to determine approximate probabilities instead of the assumption of equal likeliness. Probabilities in these experiments are defined as the ratio of the frequency of the occupance of an event, f(E), to the number of trials in the experiment, n, written symbolically as P(E) = f(E)/n. If our experiment involves flipping a coin, the empirical probability of heads is the number of heads divided by the total number of flips.

The relationship between these empirical probabilities and the theoretical probabilities is suggested by the Law of Large Numbers. It states that as the number of trials of an experiment increases, the empirical probability approaches the theoretical probability. This makes sense as we would expect that if we roll a die numerous times, each number would come up approximately 1/6 of the time. The study of empirical probabilities is known as statistics.