Empirical probability is also known as experimental probability. The empirical probability gives the likelihood of an event to happen based on the outcomes from a set of previous experiments. It is different from theoretical probability as empirical probability is dependent on the occurrence of events in a collected data.

Empirical probability of event E, P(E) = $\frac{Number\ of\ occurrences\ of\ E}{Total\ number\ of\ experiments}$

Example:

A coin was tossed 4 times and gives a head only once. Find the empirical and theoretical probability of getting a head if the coin is tossed again.

Solution:

Theoretical probability = $\frac{1}{2}$

Empirical probability = $\frac{1}{4}$

Word Problems

Problem 1:

Given table shows the numbers obtained in throw of a dice in 5 experiments. Find the probability of getting a 3 empirically.

Experiment 
Result 

Solution:

Number of experiments = 5

Number of times 3 came = 2

Empirical Probability = $\frac{2}{5}$
Problem 2:

A coin is tossed 50 times in which 32 times it gives a tail. Find the empirical and theoretical probability of getting a head.

Solution:


Total number of experiments = 50

Number of times tail has come = 50 - 32 = 18

Empirical Probability = $\frac{18}{50}$ = $\frac{9}{25}$

Total number of possible events = {H, T} = 2

Number of favorable events = {H} = 1

Theoretical probability = $\frac{1}{2}$
Problem 3:

The table below shows the grade point obtained by the students in a certain subject. Find the empirical probability of getting grade below 8.

 Grade 5
6
7
 8 9
 Number of students  34  22 17
 14  8

Solution:

Total number of students = 34 + 22 + 17 + 14 + 8 = 95

Students getting grade less than 8 = 34 + 22 + 17 =73

Empirical probability = $\frac{73}{95}$
Problem 4:

In a buffet, 78 out of 95 guests chose vanilla over chocolate ice cream. Find the empirical probability of a random guest opting for vanilla ice cream.

Solution:


Total number of data obtained = 95

Guests choosing vanilla = 78

Empirical probability = $\frac{78}{95}$