### 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}}\)

$=\frac{3}{10}=0.33$

2. Let us take the another frequency distribution table, which gives the outcome of weights of the 100 students in a class.

 Weights in Kg The 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:

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

$$=$$ $\frac{21}{100}=0.21$
In the upcoming exercises we apply this concept to determine the probability of the events.