Empirical Probability Formula

Empirical probability is also known as an experimental probability which refers to a probability that is based on historical data. In other words, simply we can say that empirical probability illustrates the likelihood of an event occurring based on historical data. In theoretical probability, we assume that the probability of occurrence of any event is equally likely, and based on that we predict the probability of an event.

The empirical probability formula can be obtained by multiplying the number of times an event occurs by the total number of trials. Let us understand the empirical probability formula using solved examples.

Note: Probability can be classified as

• Theoretical probability and
• Empirical probability

What Is Empirical Probability Formula?

The empirical probability of an event is based on what has actually happened. On the other hand, the theoretical probability of the event attempts to predict what will happen on the basis of a total number of possible outcomes. If the number of trials in an experiment goes on increasing we may expect the experimental and theoretical probabilities to be nearly the same.

The formula for empirical probability is :

Empirical Probability Formula = f/n

where,

• f is the number of times an event occurs
• n is the total number of trials

Let us understand the empirical probability formula using solved examples.

Definition of Empirical Probability

Empirical probability can be defined as the estimator of probability based on experiences and observations. The main advantage of empirical probability is that the procedure is considered free of assumptions i.e. no data is assumed or no hypotheses but is backed by experimental studies and data. Hence, it is also called experimental probability or relative frequency.

Examples Using Empirical Probability Formula

Example 1: In a group of 50 people, 32 people chose to order non-veg burgers over the veg. What is the empirical probability of someone ordering veg burgers?

Solution:
It is given that
Total number of people = 50
Number of people who chose non-veg burgers = 32
Number of people who chose veg burgers = 50 - 32 = 18

Hence,
As per empirical probability formula, it is = 18 / 50 = 0.36.

Therefore, the empirical probability of someone ordering veg burgers is 0.36 or 36%.

Example 2: A coin toss three times and the result was three heads. Using the empirical probability formula find out what is the empirical probability of getting a head?

Solution:
It is given that
Total number of trials = 3
Number of heads = 3

Hence,
Empirical probability = 3 / 3 = 1.

Therefore, the empirical probability of getting a head is 1 or 100%.

Example 3: In a buffet, 90 out of 100 people chose to order coffee over tea. What is the empirical probability of someone ordering coffee?

Solution:
It is given that
Total number of people = 3
Number of people who choose coffee or tea = 90.
Number of people who choosing coffee or tea = 100 - 90 = 10

Hence,
As per empirical probability formula, it is = 10 / 100 = 0.10.

Therefore, the empirical probability of someone ordering coffee is 0.10 or 10%.