# Empirical Probability Formula

## Empirical Probability Formula

Empirical probability is an objective probability. It is also called relative frequency or experimental probability. The definition of the Empirical Probability Formula is the number of outcomes in which a specified event occurs to the total number of trials. It is different from theoretical probability in certain major aspects. In theoretical probability, the probability is measured according to the likelihood of an outcome. However, in the case of Empirical probability, the probability is based on how the event actually occurred during trials. The Empirical Probability Formula differs from the theoretical probability in its formula.

Empirical probability Formula – what is it? This is the likelihood of an event occurring. Let’s take a simple example, such as a die. Each face of the dice has a number 1 to 6 printed on it. A dice is shaped like a cube. Every time the dice are rolled, only one face will appear. When the dice cube is rolled, only one face will have a number printed on it out of the six faces of the dice. As a result, 1 (face) divided by 6 (total number of faces) equals 16.6 = 0.1666. There is a chance or probability that a particular number will appear.

Let’s examine the word Empirical Probability Formula now. Taking the dice again, suppose we roll 120 times and want to estimate how many times the number 6 would appear. In the case of a die cube, we know that the chance of 6 coming up is 1/6 when we roll the dice once. Therefore, when rolling the dice 120 times, the probability of the number 6 coming up is 120 Empirical 1/6, which equals 20. When we roll the dice 120 times, this is the Empirical Probability Formula that the number 6 will appear.

In other words, the Empirical Probability Formula of a particular event occurring can be expressed as the estimated chance of that particular event occurring in a total series of events; or, put differently, by using a formula it becomes:

In this case, the probability is calculated by multiplying the number of times an event occurs (in this case, the number 6 appears) by the total number of trials (120 times in this case).

As a consequence, the Empirical Probability Formula of the number 6 appearing in 120 dice throws is 120 × 1/6 =20.

Experimental Probability is also known as Relative Frequency or Empirical Probability. In other words, it is the ratio of the number of cases in which a particular event occurs to the number of actual trials made, not as a theoretical calculation but as an observation of actual results. An Empirical Probability Formula is a prediction based on actual experimental observations.

The relative frequency of ‘A’ is equal to m/n if ‘A’ happens ‘m’ times out of a total of ‘n’ tries or trials.

According to statistics, it is the scientific prediction or estimate of a probability. Modelling using a Binomial Distribution can be carried out for simple cases where an experiment only determines whether an event has occurred or not. As a result, it is called the maximum likelihood estimate. If we make certain postulations or hypotheses about the prior distribution of the probability, it is called the Bayesian Estimate. One can improve the Empirical Probability Formula by assuming further data or hypotheses in case a trial provides more results or information. When we use such a model, we can derive a prediction or estimate of a particular event.

Therefore, the probability can be broadly classified as follows:

1. Theoretical Probability and
2. Empirical Probability

### Theoretical Probability and Empirical and Probability – Pros and Cons

If to estimate the probability, one uses Empirical Probability Formula, which has the advantage that it is based on actual experimental studies and does not assume any data or hypotheses.

To illustrate this, examine an example

Suppose we are asked to estimate the probability that two conditions are met by a population or group of men

(i) That they are over 6 feet tall

There must be a preference for strawberry jam instead of pineapple jam.

The Empirical Probability Formula of the combined condition can only be determined by actually counting the number of men who meet both conditions. The proportion of men who prefer strawberry jam over pineapple jam can also be calculated by multiplying the number of men who are taller than 6 feet with men over 6 feet tall. However, this type of estimation is based on the assumption that the two conditions are statistically independent.

### Mixed Classification or Nomenclature

A-posteriori probability can also be used to refer to Empirical Probability Formula or relative frequency. Its use is indicative of the terms used in Bayesian statistics, but it is not directly related to the Bayesian results achieved. The same phrase is sometimes used to refer to posterior probabilities, which are completely different, even though they have a misleadingly similar name.

The phrase ‘a-posteriori probability’ when taken to mean (or considered equivalent to) empirical probability may be used in combination with the words ‘a Priori probability’, meaning the estimate of a probability based on logical reasoning or what has been deduced without any observation or recording.