It is remarkable that a science, which began with the consideration of games of chance, should be elevated to the rank of the most important subject of human knowledge. —Pierre Simon Laplace
Mathematics has a wide range of applications in real life. It encourages analytical thinking to identify the problem and find the solution,strong brain muscles, encourages critical thinking ability, problem-solving ability and much more. Higher education becomes relatively easy once students have a conceptual understanding of the mathematical concepts covered in lower grades. Hence, Mathematics is one of the core subjects in f almost all the competitive examinations.
Probability is the study of predictions and assumptions. To master the skill of making accurate predictions , one needs to learn the art of predicting things using certain principles. Its synonyms are – possibility, prospect, odds, likely, unlikelihood, chance, likelihood, presumption, feasibility, credibility and improbability. The random experiments of probability, the process of solving different applications using probability and the role of probability in day-to-day life are some of the essential topics covered in this chapter.
The students need to have the proper knowledge of this chapter. As a result, in the NCERT Solutions for Class 9 Mathematics Chapter 15, we have covered every topic in detail with a proper analysis of each concept. It is designed by the subject matter experts who meticulously follow the CBSE curriculum and guidelines to provide concise and accurate notes to the students.Needless to say, they completely understand what is legitimate as per the board’s standards and hence it is reliable and trustworthy. Students can take note of the to-be-focused points from the chapter and use them in their mathematical calculations. Thus, they can strengthen their conceptual understanding of every topic covered in this chapter.
Extramarks believes and encourages 360° learning among students., i.e. learning based on the students’ overall development.Extramarks understands how important it is to give step-by-step explanations for making the concepts easy for students and even clarify their doubts via live classes. Moreover, it has practice questions to step up your performance and thereby prepare well for the examinations to get excellent results.
Extramarks’ website is a one stop solution to all your queries and problems. You can access all the NCERT-related resources like NCERT Solutions, NCERT Exemplar etc., from the Extramarks’ website. Moreover, these practice questions will step up your preparation significantly and help you to get excellent results in the examination. You needn’t waste your precious time looking for any kind of assistance in other subjects because Extramarks has solutions for all classes from 1 to 12. Extramarks is known for providing authentic, reliable and to the point study material and students have complete faith and trust in our services.
Key Topics Covered In Class 9 Mathematics Chapter 15
Chapter 15 Class 9 Mathematics is about Probability and its applications.
When you toss a coin, you have two chances to get a head or a tail. Thus, there is a half possibility of getting a head and a half possibility of getting a tail. This is called probability.
Probability is the study of all the possible outcomes you will get for an event. It is merely an assumptions-based study which helps in predictions in various disciplines of life. It explains how to study an event and how to draw possible outcomes from a certain event.
It encourages students to develop analytical skills and hence, they will be able to approach problems in a smarter way. The NCERT Class 9 Mathematics Chapter 15 is covered in the NCERT Solutions for Class 9 Mathematics Chapter 15 and is available on the Extramarks’ website.
Students can learn basic probability formulas on determining empirical probability and defining its limiting value. Moreover, NCERT solutions provide tips to help students to quickly learn every topic covered in the chapter. Moreover, it has practice questions to step up your performance and prepare well for the examinations to get excellent results.
Introduction
In this chapter, we will learn about probability, its meaning and the chances of an outcome. Probability is used in many fields, for example, physical sciences, commerce, biological science, medical science, weather forecast etc. All the fundamentals of probability are covered in this chapter.
We have covered all the concepts and topics in our study material, students can visit our Extramarks’ website to access NCERT Solutions for Class 9 Mathematics Chapter 15.
Probability – an experimental approach
The concept of probability was given by the French philosopher Chevalier De Mere in 1654. He did some experiments and observed their outcomes.. Most of his experiments were on coins and dice problems.
You will learn about the experiments in probability with the activities given below,
- Activity1 : It is based on an experiment on coins. Students can toss two coins and draw conclusions according to its observation.
- Activity2 : In this activity, a class is divided into groups of 2-3 students. Each group has to toss coins individually and draw conclusions according to their observations.
- Activity3 : It is based on the experiments of dice problems. Students need to toss dice and draw conclusions according to its observation.
There is an empirical formula available on probability which is given below:
[ P(E) = numbers of the trials in which the events happened / the total number of trials ]
In this chapter, there are some experiments which are available in a very detailed manner on our Extramarks’ website. Students can refer to NCERT Solutions for Class 9 Mathematics Chapter 15.
Summary
In this chapter, we have learnt about the probability
- The chapter states the history of probability and the scientist who gave the concept of probability.
- There are many applications of probability in the following areas: :
- Physical Sciences
- Commerce
- Biological Science
- Medical Science
- Weather Forecast
- Students can perform experiments on probability with the help of coins.
- In this chapter, we learnt about the empirical formula of probability.
[ P(E) = numbers of the trials in which the events happened / the total number of trials ]
In this chapter, we will get complete information regarding probability and perform some experiments on the dice and coins.. To get further details and practice the exercises related to this topic, students can access the NCERT Solutions for Class 9 Mathematics Chapter 15 from the Extramarks’ website.
NCERT Solutions for Class 9 Mathematics Chapter 15 Exercise & Solutions.
One can find all the NCERT Solutions to the exercises covered in the chapter in the NCERT Solutions for Class 9 Mathematics Chapter 15. The subject matter experts give the solutions. All the solutions are in a step-by-step format, for making the concepts easy for students and even clarify their doubts via live classes. The highlighted points from the chapter, which will help students to learn every topic covered in the chapter quickly. Moreover, it has practice questions to step up your performance and thereby prepare well for the examinations to get excellent results.
All the solutions are given point-wise for the students to quickly understand and solve mathematical problems with ease. Students can confidently rely on our learning solutions for their studies and exam preparation. It’s important to go beyond the NCERT books by including solutions as an integral part of your study schedule. This encourages the students to master the topic and increases their confidence in achieving a high grade. Students swear by Extramarks because of the absolute trust and confidence it has built over the years.
You can avail of NCERT Solutions for Class 9 Mathematics Chapter 15 from the Extramarks website.
Click on the links below to access exercise-specific questions and solutions of NCERT Solutions for Class 9 Mathematics Chapter 15:
- Chapter 15: Exercise 15.1
Along with Class 9 Mathematics Solutions, you may explore NCERT Solutions on our Extramarks’ website for all primary and secondary classes.
- NCERT Solutions Class 1
- NCERT Solutions Class 2
- NCERT Solutions Class 3
- NCERT Solutions Class 4
- NCERT Solutions Class 5
- NCERT Solutions Class 6
- NCERT Solutions Class 7
- NCERT Solutions Class 8
- NCERT Solutions Class 9
- NCERT Solutions Class 10
- NCERT Solutions Class 11
- NCERT Solutions Class 12
NCERT Exemplar Class 9 Mathematics
NCERT Exemplar Class 9 Mathematics book will help to step up your preparation by testing your problem solving and analytical skills. . It has a compilation of all the advanced level questions designed as per NCERT textbooks based on the latest CBSE syllabus. The questions follow the competitive examinations pattern. This will definitely help students in solving all types of tricky and difficult problems confidently.
It covers complex theories that confidently prepare students to face the upcoming examinations. It has plenty of examples for helping students to leverage their performance. It is a complete source of information for CBSE students preparing for their 9th standard examinations. The students think logically about a problem after referring to the NCERT Solutions and NCERT Exemplar.
They have basic as well as advanced level questions. . It contains extra questions from the NCERT Class 9 Mathematics textbook. Students can refer to NCERT Exemplar for Class 9 Mathematics for more practice. Since the difficulty level is graded, hence its important to go through NCERT syllabus first, then move to solutions and exemplar respectively.They can be rest assured that nothing remains untouched and every example solution, exercise has been covered in the chapter and hence they are confident of their preparation and to ace the exam with excellent results.
Key Features for NCERT Solutions for Class 9 Mathematics Chapter 15
Consistency during preparation is quite necessary for the students to excel. Hence, NCERT Solutions for Class 9 Mathematics Chapter 15 helps students to practice these questions on a regular basis. . Some of the key features are:
- You can find all the resources you need for revision in our NCERT Solutions for Class 9 Mathematics Chapter 15.
- It has easy-to-learn and understandable key points that help students learn fast.
- After completing the NCERT Solutions for Class 9 Mathematics Chapter 15, students will be relieved to find all the related concepts they studied in previous classes in the higher classes too.