Question

A die is rolled 300 times and following outcomes are recorded

Outcome	1	2	3	4	5	6
Frequency	42	60	55	23	60	30

 Find the probability of getting a number
(i) More than 4 (ii) Less than 3

Answer 1

Hint: A die has a shape of a cube so it has 6 sides and the outcomes possible are 1, 2, 3, 4, 5, 6. Probability can be simply defined as how likely something is to happen. Let there be an event A
$\text{Probability for an event A to occur P(A)}=\dfrac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
Here if P(A) is the probability for an event A to occur then \[0\le P(A)\le 1\]

Complete step by step answer:
(i) Firstly, let us solve the first part of the question which is probability of getting a number more than 4
Now, we will find the number of favorable outcomes of getting a number more than 4
= Number of favorable outcomes of getting 5+Number of favorable outcomes of getting 6
Number of favorable outcomes for getting 5 = 60
Number of favorable outcomes for getting 6 = 30
Total number of outcomes = 300 (as the die is rolled 300 times)
the number of favorable outcomes of getting a number more than 4 = 60 + 30 = 90
$\begin{align}
  & \text{Probability of getting a number more than 4}=\dfrac{\text{Number of favorable outcomes of getting a number more than 4}}{\text{Total number of outcomes}} \\
 & \text{ = }\dfrac{90}{300}=\dfrac{3}{10} \\
\end{align}$

Hence, the probability of getting a number more than 4 is \[\dfrac{3}{10}\].

(i) Now let us solve the second part of the question which is probability of getting a number less than 3
Now, we will find the number of favorable outcomes of getting a number less than 3
= Number of favorable outcomes of getting 1+Number of favorable outcomes of getting 2
Number of favorable outcomes for getting 1 = 42
Number of favorable outcomes for getting 2 = 60
Total number of outcomes = 300 (as the die is rolled 300 times)
the number of favorable outcomes of getting a number more than 4 = 42 + 60 = 102
$\begin{align}
  & \text{Probability of getting a number less than 3}=\dfrac{\text{Number of favorable outcomes of getting a number less than 3}}{\text{Total number of outcomes}} \\
 & \text{ = }\dfrac{102}{300}=\dfrac{17}{50} \\
\end{align}$

Hence, the probability of getting a number less than 3 is \[\dfrac{17}{50}\].

Note: If ever while solving the problem our answer that is the probability of a given event exceeds 1 then it should be known that the student has made a mistake in solving the given question and should recheck the solution as probability of any even can neither exceed 1 nor be less than 0.