Theory:

A frequency distribution table is used to display a wide range of various outcomes of the events. Applying this, we can determine the probability in the finest way.
Let us explore this concept with an example.
Example:
1. Observe the frequency distribution table, which gives the outcome of dice game.
 
Dice number\(1\)\(2\)\(3\)\(4\)\(5\)\(6\)
Frequency\(1\)\(3\)\(2\)\(1\)\(1\)\(2\)
 
Find the probability of getting dice number \(2\).
 
Solution:
 
First we find out the total number of trails.
 
The total number of trails \(=\) \(1 + 3 + 2 + 1 + 1 +2 = 10\)
 
The frequency of the dice number \(2\) is \(3\).
 
Therefore:

\(\text{The probability of getting dice number \(2\) =}\) \(\frac{\text{The frequency of the dice number \(2\)}}{\text{The total number of trails}}\)

 
=310=0.33
 
 
2. Let us take the another frequency distribution table, which gives the outcome of weights of the 100 students in a class.
 
Weights in KgThe number of students
\(40-45\)12
\(56-60\)41
\(61-70\)21
\(71-80\)17
\(81-85\)9
 
Find the probability that the weight of a student in the class lies in the interval \(61-70\) \(kg\).
 
Solution:
 
The total number of students in the class \(=\) 12+41+21+17+9 \(=\) 100.
 
The number of students with weight in the interval \(61-70\) \(kg\) is 21.
 
Therefore:

\(\text{The probability that the weight of a student in the class lies in the interval 61-70 kg =}\) \(\frac{\text{The number of students with weight in the interval 61-70 kg}}{\text{The total number of students in the class}}\)

 
\(=\) 21100=0.21
In the upcoming exercises we apply this concept to determine the probability of the events.