NCERT Solutions for Class 8 Maths Chapter 5 Data Handling (EX 5.3) Exercise 5.3

Exercise 5.3

Refer to pages 8-10 for exercise 5.3 in the PDF

1. List the outcomes you can see in these experiments.

(a) Spinning a wheel (b) Tossing two coins together

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(a) Ans: There are 4 possible outcomes. There are four letters A, B, C and D in a spinning wheel. 

(b) Ans: When two coins are tossed together. There are four possible outcomes HH, HT, TH, TT, where H and T means head and tail.

2. When a die is thrown, list the outcomes of an event of getting:

(i) (a) a prime number (b) not a prime number

(ii) (a) a number greater than 5 (b) a number not greater than 5

Ans: When a dice is thrown, the possible outcomes are 1, 2, 3, 4, 5, and 6.

(i) (a) Ans: The outcomes of getting a prime number are 2, 3 and 5.

(b) Ans: 1, 4 and 6 are not prime numbers. Outcomes of events of not getting a prime number are 1, 4 and 6.

(ii) (a) Ans: Outcomes of the event of getting a number greater than 5 is only 6.

(b) Ans: Outcomes of events of not getting a number greater than 5 are 1, 2, 3, 4 and 5.

3. Find the:

(a) Probability of the pointer stopping on D in (Question 1 (a)).

(b) Probability of getting an ace from a well shuffled deck of 52 playing cards.

(c) Probability of getting a red apple. (See figure alongside)

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(a) Ans: In a spinning wheel, there are five pointers A, A, B, C, D. So there are five outcomes. Pointer stops at D which is one outcome.

So the probability of the pointer stopping on D= \[\dfrac{1}{5}\]

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(b) Ans: There are 4 aces in a deck of 52 playing cards. So, there are four events of getting an ace.

So, probability of getting an ace =\[\dfrac{4}{{52}} = \dfrac{1}{{13}}\]

(c) Ans: Total number of apples is 7 and in that there are 4 that are red.

Probability of getting red apple =\[\dfrac{4}{7}\]

4. Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and

mixed well. One slip is chosen from the box without looking into it. What is the probability of:

(i) Getting a number 6.

(ii) Getting a number less than 6.

(iii) Getting a number greater than 6.

(iv) Getting a 1-digit number.

(i) Ans: There are 10 slips in the box and 6is written on only one slip.

Therefore, probability of getting a number 6 =\[\dfrac{1}{{10}}\]

(ii) Ans: Numbers less than 6 are 1, 2, 3, 4 and 5. So there are 5 outcomes.

Then the probability of getting a number less than 6 =\[\dfrac{5}{{10}} = \dfrac{1}{2}\]

(iii) Ans:  Number greater than 6 out of ten that are 7, 8, 9, 10. So there are 4 possible outcomes.

Therefore, probability of getting a number greater than 6 =\[\dfrac{4}{{10}} = \dfrac{2}{5}\]

(iv) Ans: One digit numbers are 1, 2, 3, 4, 5, 6, 7, 8, 9 out of ten outcomes.

Therefore, probability of getting a 1-digit number =\[\dfrac{9}{{10}}\]

5. If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting a green sector? What is the probability of getting a none-blue sector?

Ans: There are five sectors. Three sectors are green out of five sectors.

Therefore, probability of getting a green sector =\[\dfrac{3}{5}\]

There is one blue sector out of five sectors.

Non-blue sectors $ = 5 - 1 = 4$ sectors

Therefore, probability of getting a non-blue sector =\[\dfrac{4}{5}\]

6. Find the probability of the events given in Question 2.

Ans: When a die is thrown, there are a total six outcomes, i.e., 1, 2, 3, 4, 5 and 6.

(i) (a) Ans: The outcomes of the event of getting a prime number are 2, 3 and 5. So there are 3 outcomes out of 6.

Therefore, probability of getting a prime number =\[\dfrac{3}{6} = \dfrac{1}{2}\]

(b) Ans: 1, 4, 6 are not the prime numbers. So there are 3 outcomes out of 6.

Therefore, probability of getting a prime number =\[\dfrac{3}{6} = \dfrac{1}{2}\]

(ii) (a) Ans: Only 6 is greater than 5 in the possible outcomes. So there is one outcome out of 6.

Therefore, probability of getting a number greater than 5 =\[\dfrac{1}{6}\]

(b)  Ans: Out of the 6 possible outcomes the number not greater than 5 are 5.

Therefore, probability of not getting a number greater than 5 = \[\dfrac{5}{6}\]

Class 8 Chapter 5 Exercise 5.3 Data Handling – A Quick Glimpse

‘Data handling’ is an essential chapter as it paves the way to deciphering information from raw data. It is incorporated in the syllabus for Class 8 Maths to build a foundation for advanced concepts that a student is likely to deal with while pursuing higher studies.

It has extensive implications in research and data analysis in almost every field of study.  Various processes are involved in handling data, which can prove to be beneficial in several ways. For instance, confidential and high-end data can be stored and/or retrieved with the help of these.

However, for learning based in school, you need to follow your reference book carefully. Also, you can have a go-through from our NCERT Solutions for Class 8 Maths Chapter 5 Exercise 5.3 as an effective guideline. Our solutions have multiple shortcut techniques and step by step explanations for every question covered in this chapter.

Our solutions will help you –

• To develop a deeper understanding of data handling.

• To know about various parameters involved in the handling of data.

• Step by step guide to solving numerical.

• Interpreting data presented in various forms.

• Understanding the detailed explanation of the reasons behind every step.

Above all, students need to practise regularly to fetch higher grades in the exam. Combined with our appropriate solutions for NCERT Maths Class 8 Chapter 5 Exercise 5.3, you can quickly get a stronghold on the subject.

NCERT Solution of Class 8 Maths Chapter 5 Exercise 5.3 – All Questions

Here is a brief overview of the solutions covered in these exercises and what you are about to learn in them, with a particular focus on Exercise 5.3.

Class 8th Maths Chapter 5 Exercise 5.3 - Question 1

The first question has two cases provided, where you are asked to find the respective outcomes and list them. Our NCERT Solutions for Class 8 Maths Chapter 5 Exercise 5.3 explains that the key to this question is - you need to create another set of data from a given experiment. 

Here, you have to:

• Understand what the experiment demands.

• Find a sample space.

• List the total number of outcomes that are possible.

These three steps are essential in solving these types of questions, where you need to:

• Throw a dice or two simultaneously.

• Pick a specific card.

• Toss a coin or more.

• Spin a wheel.

Students should clearly understand all these concepts before delving into related questions. These are explained in our NCERT Solution of Class 8 Maths Chapter 5 Exercise 5.3 with the necessary steps.

NCERT Maths Solution Class 8 Chapter 5.3 - Question 2

Question 2 deals with a particular case of throwing dice and you are asked to list the outcomes. Specific events are listed down which you need to consider while listing.

There can be events like the following when the number appearing on the dice can be:

• A prime number.

• A composite number.

• A number divisible by any other specific number, as mentioned in the question.

• A number greater/lesser than another particular number.

You have to consider the required event as per the question, and then follow the steps mentioned earlier to find the final answer.

For a comprehensive approach to such questions, you can take a look at our NCERT Solutions for Class 8 Maths Chapter 5 Exercise 5.3. It will assist you in solving the numerical correctly as well as build a firm base on the concept.

NCERT Maths Solution Class 8 Exercise 5.3 - Question 3

This question has three events provided based on which you need to find the probability of those events occurring. The events are:

• From question 1, the probability of the wheel stopping at D.

• In the next event, you have to calculate the probability of picking a particular card.

• The last one asks to calculate the probability of picking a red apple out of the total number of apples given in the figure alongside.

To find the right probability, you are required to know the process of doing so at first. From our NCERT Solutions for Class 8 Maths Chapter 5 Exercise 5.3, you will learn that two main things are required to be evaluated initially, for instance 

• Sample space for which the event is occurring.

• Total possible outcomes.

The basic formula for finding the probability of a particular event is that you need to divide the sample space by total outcomes. Refer to our NCERT Solution for Class 8 Maths Chapter 5 Exercise 5.3 to understand this even more clearly.

It is essential to know the necessary tricks when you appear for an exam. The methods will not only save your time but also help you in fetching more marks. The formula provided in our NCERT Solutions for Class 8 Maths Chapter 5 Exercise 5.3 will help you in answering complicated questions too if asked in the exam. 

Class 8th Maths Chapter 5 Exercise 5.3 - Question 4

The fourth question has provided an experiment where ten papers are kept in a box. Each of them contains only one number written on them from 1 to 10. You are required to calculate the probability of an event occurring. The events are related to the number written on the paper.

There are four events given as:

• Greater/lesser than a number.

• Equal to a number.

• 1 or 2 digits number.

These are the possible cases for which you might be asked to answer in the exam under these questions. Hence, make sure that your concept on approaching such numerical is clear beforehand.

Our NCERT Solutions for Class 8 Maths Chapter 5 Exercise 5.3 is equipped with step by step solutions to facilitate a clear understanding. As a result, you will be readily prepared for tackling even the trickiest questions in your actual exam. 

NCERT Maths Solution Class 8 Chapter 5.3 - Question 5

The fifth question has another experiment given where you have to spin a wheel, which is divided into several colourful sectors. The sector division provided here is in the following way:

• Three green sections.

• One blue section.

• One red section.

Out of these given, you are asked to find the probability of getting a green sector and a non-blue sector. Students can have the necessary knowledge from our NCERT Solutions for Class 8 Maths Chapter 5 Exercise 5.3 that:

• The sample space for finding the probability of green should be calculated both based on a total number of green sections and the entire sections present in the wheel.

• For a non-blue section, both the green and red parts must be considered for calculation.

These are some of the basic pointers which are to be considered by students during the exam, failing which there might be errors. So, to avoid silly mistakes, ensure that you have revised, and cleared all your doubts.

NCERT Maths Solution Class 8 Exercise 5.3 - Question 6

The last question is based on the data you created in the second question. In that question, you had to list the possible outcomes, and here you have to find the probability of specific events as asked.

You should know that there is a clear difference between the experiment and the events occurring. For instance, throwing dice is an experiment; however, the outcomes (number appearing on the dice) are termed as events.

There is a short trick that our tutors recommend; it is to cross-check if your solution is right. The method is to check for whether the summation of all the probabilities for the occurrence of an event should be equal to 1.

Simply put, the probabilities are usually expressed infractions. Therefore, you need to check if all of those for a particular experiment add up to 1 one or not. It is primarily because the experiment is one as a whole, and we are finding the possibilities of various occurrences. 

You Can Understand This From The Following Simple Example:

For instance, we take a regular, unbiased coin, which has two sides – head and tail. Hence, when you toss the coin, then there can be either of the two outcomes - a head or a tail. The total possible results = 2.

Therefore, the possibility that ahead will appear is 1 out of 2. Similarly, for a tail, the chances are 1 out of 2. Now, when you add both these possibilities, you will get one as shown below.

½ + ½ = 1

So, you can see, since there are only two outcomes, the calculation becomes easier. Although for numerous outcomes, you have to do the calculations likewise, without missing any of them.

You can gain an in-depth knowledge of these from our NCERT Solutions for Class 8 Maths Chapter 5 Exercise 5.3. The explanations given there will guide you in the right way towards solving these problems. 

Class 8 Maths Chapter 5 Exercise 5.3 – Other Exercises

There are two more exercises before Exercise 5.3 in this chapter. The topics covered in those exercises are briefly described hereunder:

• Exercise 5.1: The first exercise has five questions. Here you will learn about the representation of data in various. You are likely to learn the following ways:

• Histogram

• Tally marks

• Graphs 

These three methods are essential in both description as well as deciphering information there. Data handling has a variety of applications, not only in the school level but also in higher studies and research activities too.

Hence, make sure you get a stronghold on these things from our NCERT Solutions for Class 8 Maths Chapter 5 Exercise 5.3 and other exercises for a thorough understanding. Our solutions are of standard quality and require you to read them carefully before an exam for achieving higher grades.

• Exercise 5.2: You will find five questions in this exercise, and each of them is different in terms of the presentation of data. As a result, interpreting the data rightly becomes an important task here. Only then, you can apply the appropriate method of solving the question.

• The data in questions numbered 1 and 3 are represented through a pie-chart

• The second, third and fifth questions have tabular representation.

Therefore, it shows that data can be represented in various ways. However, the key lies in deciphering necessary information from the same which can be understood from our NCERT Solutions Class 8 Maths Chapter 5 Exercise 5.3 and other exercises. The pie-charts present data where it is divided into specific sections that show the respective percentages.

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