Question

A die is rolled 300 times and the following outcomes are recorded:

Outcome	1	2	3	4	5	6
Frequency	42	60	55	53	60	30

Find the probability of getting a number
(i) more than 4
(ii) less than 3

Answer 1

Hint:Probability is the prediction or we can say that the probability is the prediction of the occurrence of an event .
Probability is defined as the ratio of the favorable events to the total number of events.
$P\left( N \right) \Rightarrow \dfrac{{\text favorable\ event}}{{total\ events}}$( Probability of event N)
The table given in the question above will help us in determining the values of the favorable events.
Using this definition of probability we will find the probability of the two events given in the question.

Complete step-by-step answer:
Let us discuss probability in much more detail to do the calculation work.
Probability predicts how likely an event is going to occur or how likely the proposition is true. Probability of an event is always less than 1 or 1, which indicates the certainty of an event and if the probability of an event is zero it means that the impossibility of an event does exist. Higher is the probability of an event more likely an event is going to occur.
Now, we will calculate the probability;
(i) When the outcome is more than 4
As per the table in the question above, more than 4 is 5 and 6 whose frequencies add up to;
$ \Rightarrow 60 + 30 = 90$
Total number of times the die is rolled is 300
Therefore, probability of more than 4 is;
$ \Rightarrow P(n) = \dfrac{{90}}{{300}}$ (90 is the favorable event)
$ \Rightarrow \dfrac{3}{{10}}$
(ii) less than 3
Less than 3 is 1 and 2
Frequencies of 1 and 2 according to the table given in the question, add up to give:
$ \Rightarrow 42 + 60 = 102$ (102 is the favorable event )
Therefore probability of less than 3 is;
$ \Rightarrow P(n) = \dfrac{{102}}{{300}}$ ( on further cancelling the fraction )

$ \Rightarrow \dfrac{{17}}{{50}}$

Note:
We have a large number of applications of probability in everyday life such as, a probabilistic approach is used by Casino players, used by many insurance policy makers and in share markets probability of rise and fall of the prizes of the shares is made by the businessmen etc.