# Empirical Probability Formula

Empirical probability is an objective probability. It is also known as relative frequency or experimental probability.

By definition, Empirical Probability is the number of outcomes in which a specified event occurs to the total number of trials.

Empirical probability is different from Theoretical probability on certain major aspects. That is, in theoretical probability, the probability is measured on the basis of the likeliness of an outcome. Whereas in the case of Empirical probability, the probability is based on how the event actually occurred during trials. The formula for Empirical probability is unlike a theoretical probability formula.

$\large P(E)=\frac{Number\;of\;times\;event\;occurs}{Total\;number\;of\;times\;experiment\;performed}$

$\large P(E)=\frac{f}{n}$

P(E) = Empirical Probability

### Solved Examples

Question: Calculate the empirical probability of an event wherein 40 is the frequency of the class and 120 is the total frequencies in the probability distribution?

Solution:

Given; f = 40, n = 120

Using formula,
P(E) = $\frac{f}{n}$
P(E) = $\frac{40}{120}$
P(E) = 0.33333

#### Practise This Question

Radius of a circle is doubled. What will be the ratio of areas of the new circle to the area of the given circle?