probability case study examples class 9

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Class 9th Maths - Probability Case Study Questions and Answers 2022 - 2023

Class 9th Maths - Probability Case Study Questions and Answers 2022 - 2023 Study Materials Sep-08 , 2022

QB365 provides a detailed and simple solution for every Possible Case Study Questions in Class 9th Maths Subject - Probability, CBSE. It will help Students to get more practice questions, Students can Practice these question papers in addition to score best marks.

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Probability case study questions with answer key.

Final Semester - June 2015

(b) Find the probability that the bead drawn by her is not green.

(c) Find the probability that she draws either a green or a blue bead.

(d) Find the probability that she draws neither a red nor a green bead.

(e) Which of the following is an impossible event? (i) The bead drawn is not red (ii) The bead drawn is neither red nor blue (iii) The bead drawn is either red or green or blue. (vi) The bead drawn is yellow.

(ii) If the card drawn in first case is replaced,  and the second boy draws a card.  What is the probability getting a prime number?

(

(iii) If the card drawn, is not replaced in the second draw, what is the probability that he got a multiple of 3 greater than 4?

(iv) For a sure event A, P(A) = ?

(v) If all cards drawn are replaced then what is the probability of getting a multiple of 3 and 5?

(b) Find the probability that the arrow will point at an even number.

(c) Find the probability that the arrow will point at a prime number.

(d) Find the probability that the arrow will point at a number divisible by 3.

(e) Find the probability that the arrow will point at a number greater than 2.

(b) Find the probability that lost piece is square.

(c) Find the probability that lost piece is triangle.

(d) Find the probability that lost piece is square of blue color.

(e) Find the probability that lost piece is triangle of red color.

(ii) A player will get a special prize, if spinner stops on a perfect square:

(iii) If the player gets a chance to throw, a dice, what is the probability of getting a multiple of 2 on dice?

(iv) If a dice is thrown, what is the probability of getting a number less than 4?

(v) An event whose probability to occur is 1. Then this type of event is called:

(ii) The number of red pens in the box are:

(iii) Probability of taking blue pen is:

(v) Probability of taking blue or green pen is:

(

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CBSE Class 9 Mathematics Case Study Questions

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If you’re looking for a comprehensive and reliable study resource and case study questions for class 9 CBSE, myCBSEguide is the perfect door to enter. With over 10,000 study notes, solved sample papers and practice questions, it’s got everything you need to ace your exams. Plus, it’s updated regularly to keep you aligned with the latest CBSE syllabus . So why wait? Start your journey to success with myCBSEguide today!

Significance of Mathematics in Class 9

Mathematics is an important subject for students of all ages. It helps students to develop problem-solving and critical-thinking skills, and to think logically and creatively. In addition, mathematics is essential for understanding and using many other subjects, such as science, engineering, and finance.

CBSE Class 9 is an important year for students, as it is the foundation year for the Class 10 board exams. In Class 9, students learn many important concepts in mathematics that will help them to succeed in their board exams and in their future studies. Therefore, it is essential for students to understand and master the concepts taught in Class 9 Mathematics .

Case studies in Class 9 Mathematics

A case study in mathematics is a detailed analysis of a particular mathematical problem or situation. Case studies are often used to examine the relationship between theory and practice, and to explore the connections between different areas of mathematics. Often, a case study will focus on a single problem or situation and will use a variety of methods to examine it. These methods may include algebraic, geometric, and/or statistical analysis.

Example of Case study questions in Class 9 Mathematics

The Central Board of Secondary Education (CBSE) has included case study questions in the Class 9 Mathematics paper. This means that Class 9 Mathematics students will have to solve questions based on real-life scenarios. This is a departure from the usual theoretical questions that are asked in Class 9 Mathematics exams.

The following are some examples of case study questions from Class 9 Mathematics:

Class 9 Mathematics Case study question 1

There is a square park ABCD in the middle of Saket colony in Delhi. Four children Deepak, Ashok, Arjun and Deepa went to play with their balls. The colour of the ball of Ashok, Deepak,  Arjun and Deepa are red, blue, yellow and green respectively. All four children roll their ball from centre point O in the direction of   XOY, X’OY, X’OY’ and XOY’ . Their balls stopped as shown in the above image.

Answer the following questions:

Answer Key:

Class 9 Mathematics Case study question 2

• Now he told Raju to draw another line CD as in the figure
• The teacher told Ajay to mark  ∠ AOD  as 2z
• Suraj was told to mark  ∠ AOC as 4y
• Clive Made and angle  ∠ COE = 60°
• Peter marked  ∠ BOE and  ∠ BOD as y and x respectively

Now answer the following questions:

• 2y + z = 90°
• 2y + z = 180°
• 4y + 2z = 120°
• (a) 2y + z = 90°

Class 9 Mathematics Case study question 3

• (a) 31.6 m²
• (c) 513.3 m³
• (b) 422.4 m²

Class 9 Mathematics Case study question 4

How to Answer Class 9 Mathematics Case study questions

To crack case study questions, Class 9 Mathematics students need to apply their mathematical knowledge to real-life situations. They should first read the question carefully and identify the key information. They should then identify the relevant mathematical concepts that can be applied to solve the question. Once they have done this, they can start solving the Class 9 Mathematics case study question.

Students need to be careful while solving the Class 9 Mathematics case study questions. They should not make any assumptions and should always check their answers. If they are stuck on a question, they should take a break and come back to it later. With some practice, the Class 9 Mathematics students will be able to crack case study questions with ease.

Class 9 Mathematics Curriculum at Glance

At the secondary level, the curriculum focuses on improving students’ ability to use Mathematics to solve real-world problems and to study the subject as a separate discipline. Students are expected to learn how to solve issues using algebraic approaches and how to apply their understanding of simple trigonometry to height and distance problems. Experimenting with numbers and geometric forms, making hypotheses, and validating them with more observations are all part of Math learning at this level.

The suggested curriculum covers number systems, algebra, geometry, trigonometry, mensuration, statistics, graphing, and coordinate geometry, among other topics. Math should be taught through activities that include the use of concrete materials, models, patterns, charts, photographs, posters, and other visual aids.

CBSE Class 9 Mathematics (Code No. 041)

I	NUMBER SYSTEMS	10
II	ALGEBRA	20
III	COORDINATE GEOMETRY	04
IV	GEOMETRY	27
V	MENSURATION	13
VI	STATISTICS & PROBABILITY	06

Class 9 Mathematics question paper design

The CBSE Class 9 mathematics question paper design is intended to measure students’ grasp of the subject’s fundamental ideas. The paper will put their problem-solving and analytical skills to the test. Class 9 mathematics students are advised to go through the question paper pattern thoroughly before they start preparing for their examinations. This will help them understand the paper better and enable them to score maximum marks. Refer to the given Class 9 Mathematics question paper design.

QUESTION PAPER DESIGN (CLASS 9 MATHEMATICS)

1.	Exhibit memory of previously learned material by recalling facts, terms, basic concepts, and answers.  Demonstrate understanding of facts and ideas by organizing, comparing, translating, interpreting, giving descriptions, and stating main ideas	43	54
2.	Solve problems to new situations by applying acquired knowledge, facts, techniques and rules in a different way.	19	24
3.	Examine and break information into parts by identifying motives or causes. Make inferences and find evidence to support generalizations Present and defend opinions by making judgments about information, validity of ideas, or quality of work based on a set of criteria. Compile information together in a different way by combining elements in a new pattern or proposing alternative solutions	18	22
		80	100

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Class 9 is an important milestone in a student’s life. It is the last year of high school and the last chance to score well in the CBSE board exams. myCBSEguide is the perfect platform for students to get started on their preparations for Class 9 Mathematics. myCBSEguide provides comprehensive study material for all subjects, including practice questions, sample papers, case study questions and mock tests. It also offers tips and tricks on how to score well in exams. myCBSEguide is the perfect door to enter for class 9 CBSE preparations.

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16 thoughts on “CBSE Class 9 Mathematics Case Study Questions”

This method is not easy for me

aarti and rashika are two classmates. due to exams approaching in some days both decided to study together. during revision hour both find difficulties and they solved each other’s problems. aarti explains simplification of 2+ ?2 by rationalising the denominator and rashika explains 4+ ?2 simplification of (v10-?5)(v10+ ?5) by using the identity (a – b)(a+b). based on above information, answer the following questions: 1) what is the rationalising factor of the denominator of 2+ ?2 a) 2-?2 b) 2?2 c) 2+ ?2 by rationalising the denominator of aarti got the answer d) a) 4+3?2 b) 3+?2 c) 3-?2 4+ ?2 2+ ?2 d) 2-?3 the identity applied to solve (?10-?5) (v10+ ?5) is a) (a+b)(a – b) = (a – b)² c) (a – b)(a+b) = a² – b² d) (a-b)(a+b)=2(a² + b²) ii) b) (a+b)(a – b) = (a + b

MATHS PAAGAL HAI

All questions was easy but search ? hard questions. These questions was not comparable with cbse. It was totally wastage of time.

Where is search ? bar

maths is love

Can I have more questions without downloading the app.

I love math

Hello l am Devanshu chahal and l am an entorpinior. I am started my card bord business and remanded all the existing things this all possible by math now my business is 120 crore and my business profit is 25 crore in a month. l find the worker team because my business is going well Thanks

I am Riddhi Shrivastava… These questions was very good.. That’s it.. ..

For challenging Mathematics Case Study Questions, seeking a writing elite service can significantly aid your research. These services provide expert guidance, ensuring your case study is well-researched, accurately analyzed, and professionally written. With their assistance, you can tackle complex mathematical problems with confidence, leading to high-quality academic work that meets rigorous standards.

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Case Study Questions for Class 9 Maths

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Are you preparing for your Class 9 Maths board exams and looking for an effective study resource? Well, you’re in luck! In this article, we will provide you with a collection of Case Study Questions for Class 9 Maths specifically designed to help you excel in your exams. These questions are carefully curated to cover various mathematical concepts and problem-solving techniques. So, let’s dive in and explore these valuable resources that will enhance your preparation and boost your confidence.

Join our Telegram Channel, there you will get various e-books for CBSE 2024 Boards exams for Class 9th, 10th, 11th, and 12th.

CBSE Class 9 Maths Board Exam will have a set of questions based on case studies in the form of MCQs. The CBSE Class 9 Mathematics Question Bank on Case Studies, provided in this article, can be very helpful to understand the new format of questions. Share this link with your friends.

If you want to want to prepare all the tough, tricky & difficult questions for your upcoming exams, this is where you should hang out.  CBSE Case Study Questions for Class 9  will provide you with detailed, latest, comprehensive & confidence-inspiring solutions to the maximum number of Case Study Questions covering all the topics from your  NCERT Text Books !

Table of Contents

CBSE Class 9th – MATHS: Chapterwise Case Study Question & Solution

Case study questions are a form of examination where students are presented with real-life scenarios that require the application of mathematical concepts to arrive at a solution. These questions are designed to assess students’ problem-solving abilities, critical thinking skills, and understanding of mathematical concepts in practical contexts.

Chapterwise Case Study Questions for Class 9 Maths

Case study questions play a crucial role in the field of mathematics education. They provide students with an opportunity to apply theoretical knowledge to real-world situations, thereby enhancing their comprehension of mathematical concepts. By engaging with case study questions, students develop the ability to analyze complex problems, make connections between different mathematical concepts, and formulate effective problem-solving strategies.

• Case Study Questions for Chapter 1 Number System
• Case Study Questions for Chapter 2 Polynomials
• Case Study Questions for Chapter 3 Coordinate Geometry
• Case Study Questions for Chapter 4 Linear Equations in Two Variables
• Case Study Questions for Chapter 5 Introduction to Euclid’s Geometry
• Case Study Questions for Chapter 6 Lines and Angles
• Case Study Questions for Chapter 7 Triangles
• Case Study Questions for Chapter 8 Quadilaterals
• Case Study Questions for Chapter 9 Areas of Parallelograms and Triangles
• Case Study Questions for Chapter 10 Circles
• Case Study Questions for Chapter 11 Constructions
• Case Study Questions for Chapter 12 Heron’s Formula
• Case Study Questions for Chapter 13 Surface Area and Volumes
• Case Study Questions for Chapter 14 Statistics
• Case Study Questions for Chapter 15 Probability

The above  Case studies for Class 9 Mathematics will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 9 Maths Case Studies have been developed by experienced teachers of schools.studyrate.in for benefit of Class 10 students.

• Class 9 Science Case Study Questions
• Class 9 Social Science Case Study Questions

How to Approach Case Study Questions

When tackling case study questions, it is essential to adopt a systematic approach. Here are some steps to help you approach and solve these types of questions effectively:

• Read the case study carefully: Understand the given scenario and identify the key information.
• Identify the mathematical concepts involved: Determine the relevant mathematical concepts and formulas applicable to the problem.
• Formulate a plan: Devise a plan or strategy to solve the problem based on the given information and mathematical concepts.
• Solve the problem step by step: Apply the chosen approach and perform calculations or manipulations to arrive at the solution.
• Verify and interpret the results: Ensure the solution aligns with the initial problem and interpret the findings in the context of the case study.

Tips for Solving Case Study Questions

Here are some valuable tips to help you effectively solve case study questions:

• Read the question thoroughly and underline or highlight important information.
• Break down the problem into smaller, manageable parts.
• Visualize the problem using diagrams or charts if applicable.
• Use appropriate mathematical formulas and concepts to solve the problem.
• Show all the steps of your calculations to ensure clarity.
• Check your final answer and review the solution for accuracy and relevance to the case study.

Benefits of Practicing Case Study Questions

Practicing case study questions offers several benefits that can significantly contribute to your mathematical proficiency:

• Enhances critical thinking skills
• Improves problem-solving abilities
• Deepens understanding of mathematical concepts
• Develops analytical reasoning
• Prepares you for real-life applications of mathematics
• Boosts confidence in approaching complex mathematical problems

Case study questions offer a unique opportunity to apply mathematical knowledge in practical scenarios. By practicing these questions, you can enhance your problem-solving abilities, develop a deeper understanding of mathematical concepts, and boost your confidence for the Class 9 Maths board exams. Remember to approach each question systematically, apply the relevant concepts, and review your solutions for accuracy. Access the PDF resource provided to access a wealth of case study questions and further elevate your preparation.

Q1: Can case study questions help me score better in my Class 9 Maths exams?

Yes, practicing case study questions can significantly improve your problem-solving skills and boost your performance in exams. These questions offer a practical approach to understanding mathematical concepts and their real-life applications.

Q2: Are the case study questions in the PDF resource relevant to the Class 9 Maths syllabus?

Absolutely! The PDF resource contains case study questions that align with the Class 9 Maths syllabus. They cover various topics and concepts included in the curriculum, ensuring comprehensive preparation.

Q3: Are the solutions provided for the case study questions in the PDF resource?

Yes, the PDF resource includes solutions for each case study question. You can refer to these solutions to validate your answers and gain a better understanding of the problem-solving process.

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CBSE Case Study Questions Class 9 Maths Chapter 15 Probability PDF Download

CBSE Case Study Questions Class 9 Maths Chapter 15  are very important to solve for your exam. Class 9 Maths Chapter 15 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving  case study-based questions for Class 9 Maths  Chapter 15 Probability

Case Study Questions Class 9 Maths Chapter 15 Probability

Case Study/Passage-Based Questions

Case Study 1: A jeweler has different types of bracelets in his shop. Sunita wants to purchase a bracelet for her sister’s birthday gift. When Sunita goes to the shop, she founds the following data which represents the number of bracelets of different types in the shop.

Find the probability that Sunita chooses Chain Bracelet. (a) 23/180 (b) 37/180 (c) 37/90 (d) 23/90

Answer: (b) 37/180

Find the probability that she chooses Pearl bracelet. (a) 23/180 (b) 37/180 (c) 37/90 (d) 23/90

Answer: (d) 23/90

What is the probability of a sure event? (a) 1 (b) 0 (c) 1/2 (d) 2/3

Answer: (a) 1

What is the probability that she chooses neither Bangle bracelet nor Pearl bracelet? (a) 23/180 (b) 45/180 (c) 109/180 (d) 23/45

Answer: (c) 109/180

What is the probability that Sunita purchased a Cuff bracelet? (a) 6/17(b)2/13 (c) 1 (d) 2/15

Answer: (d) 2/15

Case Study 2: In a factory, the workers are paid on a daily basis. The new manager wants to know the salary slab of the workers and finds the data given below.

Now, if a worker is chosen at random, then :

The probability that the worker is getting at most ₹ 500 is (a) 3/80 (b) 9/80 (c) 1/80 (d) 4/25

Answer: (b) 9/80

The probability that the worker is getting at least ₹ 701 is (a) 23/80 (b) 43/80 (c) 41/80 (d) 61/80

Answer: (b) 43/80

Probability that the worker is getting at most ₹ 900 is (a)7/40 (b) 3/31 (c) 31/40 (d) 4/31

Answer: (c) 31/40

Case Study 3: A group of students is studying probability in their math class. They encountered the following scenario:

Rajesh and Aisha decided to conduct an experiment with a deck of playing cards to understand the concept of probability. They made the following observations:

• Rajesh drew a card from a standard deck of 52 playing cards and found that it was a spade.
• Aisha drew a card from the same deck and found that it was a face card (king, queen, or jack).

Based on this information, the students were asked to analyze the probabilities of their respective outcomes. Let’s see if you can answer the questions correctly:

MCQ Questions:

Q1. The probability of drawing a spade card, as observed by Rajesh, is: (a) 1/4 (b) 1/13 (c) 1/52 (d) Cannot be determined

Answer: (a) 1/4

Q2. The probability of drawing a face card, as observed by Aisha, is: (a) 3/13 (b) 4/13 (c) 1/13 (d) Cannot be determined

Answer: (a) 3/13

Q3. In a standard deck of playing cards, the probability of drawing a spade card is: (a) 1/4 (b) 1/13 (c) 1/52 (d) 1/2

Q4. In a standard deck of playing cards, the probability of drawing a face card is: (a) 3/13 (b) 4/13 (c) 1/13 (d) 1/4

Answer: (b) 4/13

Q5. If Rajesh drew a card and found that it was a spade, what is the probability that it is also a face card? (a) 1/13 (b) 3/13 (c) 1/4 (d) 1/2

Answer: (c) 1/4

Hope the information shed above regarding Case Study Questions Class 9 Maths Chapter 15 Probability with Answers Pdf free download has been useful to an extent. If you have any other queries about CBSE Case Study Questions Class 9 Maths Chapter 15 Probability Case Study and Passage Based Questions with Answers, feel free to comment below so that we can revert back to us at the earliest possible By Team CBSEExperts

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NCERT Solutions for Class 9 Maths Chapter 15 Probability

NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1 are part of NCERT Solutions for Class 9 Maths . Here we have given NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1.

NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1

Ex 15.1 Class 9 Maths Question 1. In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary. Solution: Here, the total number of trials = 30 ∵ Number of times, the ball touched the boundary =6 ∴ Number of times, the ball missed the boundary = 30 – 6 = 24 Let the event of not hitting the boundary be represented by E, then \(P(E)=\frac { [No.of\quad times\quad the\quad batswoman\quad did\quad not\quad hit\quad the\quad boundary] }{ [Total\quad number\quad of\quad balls\quad she\quad played] } =\quad \frac { 24 }{ 30 } \quad =\quad \frac { 4 }{ 5 }\) Thus, the required probability = \(\frac { 4 }{ 5 }\)

(i) ∵ Number of families having 2 girls = 475 ∴ Probability of selecting a family having 2 girls = \(\frac { 475 }{ 1500 } \quad =\quad \frac { 19 }{ 60 }\)

(ii) ∵ Number of families having 1 girl = 814 ∴ Probability of selecting a family having 1 girl = \(\frac { 814 }{ 1500 } \quad =\quad \frac { 407 }{ 750 }\)

(iii) Number of families having no girl = 211 Probability of selecting a family having no girl = \(\frac { 211 }{ 1500 }\) Now, the sum of the obtained probabilities \(\quad =\frac { 19 }{ 60 } +\frac { 407 }{ 750 } +\frac { 211 }{ 1500 } =\frac { 475+814+211 }{ 1500 } =\frac { 1500 }{ 1500 } =1\) i.e., Sum of the above probabilities is 1.

(ii) ∵ Number of families earning Rs. 16000 or more per month and owning exactly 1 vehicle = 579 ∴ Probability of a family earning Rs. 16000 or more per month and owning exactly 1 vehicle = \(\frac { 579 }{ 2400 }\)

(iii) ∵ Number of families earning less than Rs. 7000 per month and do not own any vehicle = 10 ∴ Probability of a family earning less than Rs. 7000 per month and does not own any vehicle = \(\frac { 10 }{ 2400 }\) = \(\frac { 1 }{ 240 }\)

(iv) ∵ Number of families earning Rs. 13000 – Rs. 16000 per month and owning more than 2 vehicles = 25 ∴ Probability of a family earning Rs. 13000 – Rs. 16000 per month and owning more than 2 vehicles = \(\frac { 25 }{ 2400 }\) = \(\frac { 1 }{ 96 }\)

(v) ∵ Number of families owning not more than 1 vehicle = [Number of families having no vehicle] + [Number of families having only 1 vehicle] = [10 + 1 + 2 + 1] + [160 + 305 + 535 + 469 + 579] = 14 + 2048 = 2062 ∴ Probability of a family owning not more than 1 vehicle = \(\frac { 2062 }{ 2400 }\) = \(\frac { 1031 }{ 1200 }\)

(ii) From the given table, number of students who obtained marks 60 or above = [Number of students in class-interval 60 – 70] + [Number of students in the class interval 70 – above] = 15 + 8 = 23 ∴ Probability of a student who obtained 23 marks 60 or above = \(\frac { 23 }{ 90 }\)

(ii) ∵ Number of students who do not like statistics = 65 ∴ Probability of selecting a student who does not like statistics = \(\frac { 60 }{ 200 }\) = \(\frac { 13 }{ 40 }\)

(i) ∵ Number of engineers who are living less than 7 km from their work place = 9 ∴ Probability of an engineer who is living less than 7 km from her place of work = \(\frac { 9 }{ 40 }\)

(ii) ∵ Number of engineers living at a distance more than or equal to 7 km from their work place = 31 ∴ Probability of an engineer who is living at distance more than or equal to 7 km from her place of work = \(\frac { 31 }{ 40 }\)

(iii) ∵ The number of engineers living within \(\frac { 1 }{ 2 }\)km from their work place = 0 ∴ Probability of an engineer who is living within \(\frac { 1 }{ 2 }\)km from her place of work = \(\frac { 0 }{ 40 }\) = 0

Ex 15.1 Class 9 Maths Question 9. Activity: Note the frequency of two-wheelers, three-wheelers and four-wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two-wheeler? Solution: It is an activity. Students can do it themselves.

Ex 15.1 Class 9 Maths Question 10. Activity : Ask all the students in your class to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by 3? Remember that a number is divisible by 3, if the sum of its digit is divisible by 3. Solution: A class room activity for students.

Ex 15.1 Class 9 Maths Question 11. Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg) 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00 Find the probability that any of these bags,chosen at random contains more than 5 kg of flour. Solution: Here, total number of bags = 11 ∵ Number of bags having more than 5 kg of flour = 7 ∴ Probability of a bag having more than 5 kg of flour = \(\frac { 7 }{ 11 }\)

Ex 15.1 Class 9 Maths Question 13. The blood groups of 30 students of class VIII are recorded as follows A, B, 0, 0, AB, 0, A, 0, B, A, 0, B, A, 0, 0, A, AB, 0, A, A, 0, 0, AB, B, A, B, 0 You were asked to prepare a frequency distribution table regarding the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group AB. Solution: Here, total number of students = 30 ∵ Number of students having blood group AB = 3 ∴ Probability of a student whose blood group is AB = \(\frac { 3 }{ 30 }\) = \(\frac { 1 }{ 10 }\).

NCERT Solutions for Class 9 Maths Chapter 15 Probability (Hindi Medium) Ex 15.1

NCERT Solutions for Class 9 Maths

• Chapter 1 Number systems
• Chapter 2 Polynomials
• Chapter 3 Coordinate Geometry
• Chapter 4 Linear Equations in Two Variables
• Chapter 5 Introduction to Euclid Geometry
• Chapter 6 Lines and Angles
• Chapter 7 Triangles
• Chapter 8 Quadrilaterals
• Chapter 9 Areas of Parallelograms and Triangles
• Chapter 10 Circles
• Chapter 11 Constructions
• Chapter 12 Heron’s Formula
• Chapter 13 Surface Areas and Volumes
• Chapter 14 Statistics
• Chapter 15 Probability
• Class 9 Maths (Download PDF)

We hope the NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1 help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1, drop a comment below and we will get back to you at the earliest.

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Test: Probability- Case Based Type Questions - Class 9 MCQ

10 questions mcq test - test: probability- case based type questions, the number of road accidents in the first six months of the year (january to june) were around 1,60,000, 35% less than the average number of accidents reported in the corresponding period in the previous six years, an obvious result of a nationwide lockdown imposed in march to slow the spread of the covid-19 infection. the number of people who died also dropped by 30% this year. a survey was held on 200 drivers in a city with the aim to find the relationship between ages and accidents. number of accidents in 4 weeks was recorded. look at the table and answer the following : q. find the probability of the event for a driver chosen at random from the city being above 50 years and having no accidents..

Total drivers = 200

P(E) = 15/200

The number of road accidents in the first six months of the year (January to June) were around 1,60,000, 35% less than the average number of accidents reported in the corresponding period in the previous six years, an obvious result of a nationwide lockdown imposed in March to slow the spread of the Covid-19 infection. The number of people who died also dropped by 30% this year. A survey was held on 200 drivers in a city with the aim to find the relationship between ages and accidents. Number of accidents in 4 weeks was recorded. Look at the table and answer the following : Q. Find the probability of the event for a driver chosen at random from the city being 30 – 50 years of age and having 1 or more accidents.

= 20 + 14 + 11 = 45

Total number of drivers = 200

Required probability = 45/200

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The number of road accidents in the first six months of the year (January to June) were around 1,60,000, 35% less than the average number of accidents reported in the corresponding period in the previous six years, an obvious result of a nationwide lockdown imposed in March to slow the spread of the Covid-19 infection. The number of people who died also dropped by 30% this year. A survey was held on 200 drivers in a city with the aim to find the relationship between ages and accidents. Number of accidents in 4 weeks was recorded. Look at the table and answer the following : Q. Find the probability of the event for a driver chosen at random from the city being 18 – 30 years of age and having exactly 2 accidents.

Required probability = 37/200

The number of road accidents in the first six months of the year (January to June) were around 1,60,000, 35% less than the average number of accidents reported in the corresponding period in the previous six years, an obvious result of a nationwide lockdown imposed in March to slow the spread of the Covid-19 infection. The number of people who died also dropped by 30% this year.

A survey was held on 200 drivers in a city with the aim to find the relationship between ages and accidents. Number of accidents in 4 weeks was recorded.

Look at the table and answer the following :

Q. Find the probability of the event for a driver chosen at random from the city being above 50 years and having above 2 accidents.

Required probability = 5/200

Q. If probability of having an event is 2/3 , then what is the probability of not having that event?

Thus, required probability

Van Mahotsava is a tree planting festival which is celebrated annually in the month of July. During this festival thousands of trees are planted all over India. The name Van Mahotsava means 'the festival of trees'.

In a school, Van Mahotsava was celebrated. 250 students took part in the festival with zeal and helped each other in planting trees. Look at the table given below.

Now, Answer the following :

Q. Find the probability of planting Chameli and Rose.

No. of total plants = 100

probability = 48/100

Q. Find the probability of planting Jasmine.

Total plants = 100

probability = 24/100

Q. Find the probability of planting Marigold.

probability = 28/100

Q. Find the probability of not planting Rose .

No. of other plants = 100 – 32 = 68

Probability of planting plants other then rose = 68/100

Q. Find the sum of probability of planting Rose, Marigold, Chameli and Jasmine.

Sum of probability of planting Rose + Marigold + Chameli + Jasmine

--> and get INR 200 additional OFF

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Case Study Questions for Class 9 Maths Chapter 12 Herons Formula

Case study questions for class 9 maths chapter 9 areas of parallelograms and triangles, case study questions for class 9 maths chapter 6 lines and angles, case study questions for class 9 maths chapter 7 triangles, case study questions for class 9 maths chapter 5 introduction to euclid’s geometry, case study and passage based questions for class 9 maths chapter 14 statistics, case study questions for class 9 maths chapter 1 real numbers, case study questions for class 9 maths chapter 4 linear equations in two variables, case study questions for class 9 maths chapter 3 coordinate geometry, case study questions for class 9 maths chapter 15 probability, case study questions for class 9 maths chapter 13 surface area and volume, case study questions for class 9 maths chapter 10 circles, case study questions for class 9 maths chapter 9 quadrilaterals, case study questions for class 9 maths chapter 2 polynomials.

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Probability class 9: definition and examples - maths notes.

In this blog, we will discuss probability. We know that probability is that part of mathematics that deals with the area of uncertainty. Like on tossing a coin we get head or tail, will India win the toss or not, whether it will rain or not. Learn more about probability class 9.

Though probability started with gambling, it has been used extensively in the fields of Physical Sciences, Commerce, Biological Sciences, Medical Sciences, Weather Forecasting, etc. The probability is a number assigned to an event that tells us the chances of occurring that event.

To check the probability we have an experiment. The experiment is a situation involving chance or probability that leads to an outcome. An outcome is a result of a single trial of an experiment. Throwing a coin getting head is an outcome. On throwing dice getting 6 is an outcome. Each outcome or collection of outcomes makes an event.

Based on what we directly observe as the outcomes of our trials, we find the experimental or empirical probability. Let n be the total number of trials. The empirical probability P(E) of an event E happening, is given by Probability of E = Number of trials in which the event happened upon The total number of trials.

Probability Class 9 - Example 1

Sudha, Rahul, Gopal, Rajani, Keshav and Anuj are appearing for an audition test which is being held to select an anchor for annual function. What is the probability of selecting Gopal?

Here the total number of students is 6. Number of trials in which the event happened is 1. So Probability of E = 1 by 6.

Ok, What is the probability of any of the girls being selected? Total number of students = 6 Total number of girls = 2 So Probability of girls= number of girls upon total number of students that is 2 by 6.

Now, what is the probability of selecting a boy? Number of boys = 4 Probability of boy = number of boys upon total number students that is4 by6.

If the number of boys changes from 4 to 11 and total number of students become 23 then the probability of selecting a boy will be�.. Then Probability of boy = number of boys upon total number students which is 11 by 23.

Note that this probability kept changing depending on the number of trials and the number of total events. As in the above example, we observed that the Probability of the boy changes. Earlier it was 4 by 6 later it became 11 by 23. As the number of boys and the number of students changes the probability changes.

Probability Class 9 - Example 2

A coin is tossed 1000 times with the following frequencies: Head : 455, Tail : 545. Compute the probability for each event.

Solution: Since the coin is tossed 1000 times, the total number of trials is 1000. Let us call the events of getting a head and of getting a tail as E and F, respectively. Then, the number of times E happens, i.e., the number of times a head come up, is 455.

So, the probability of E = Number of heads upon Total number of trials i.e., Probability of E = 455/1000 = 0.455.

Similarly, the probability of the event of getting a tail = Number of tails upon Total number of trials i.e., Probability of F= 545/1000 = 0.545

Note that in the example, probability of E + Probability of F = 0.455 + 0.545 = 1, and E and F are the only two possible outcomes of each trial.

Probability Class 9 - Example 3

A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given in the following table: Find the probability of getting each outcome.

Solution : Let Ei denote the event of getting the outcome i, where i = 1, 2, 3, 4, 5, 6. Then Probability of the outcome 1 = Probability of E1 =Frequency of 1upon Total number of times the die is thrown = 179/1000 = 0.179 Similarly, Probability of E2 =150/1000=0.15,

Probability of E3 =157/1000 = 0.157, Probability of E4 = 149/1000 = 0.149, Probability of E5 = 175/1000 = 0.175 Probability of E6= 190/1000 = 0.19 Note that Probability of E1 + Probability of E2 + Probability of E3 + Probability of E4 + Probability of E4 + Probability of E6= 1

Also note that: (i) The probability of each event lies between 0 and 1. (ii) The sum of all the probabilities is 1. (iii) E1, E2, . . ., E6 cover all the possible outcomes of a trial.

Example: Fifty seeds were selected at random from each of 5 bags of seeds, and were kept under standardized conditions favourable to germination. After 20 days, the number of seeds that had germinated in each collection was counted and recorded as follows:

What is the probability of germination of (i) more than 40 seeds in a bag? (ii) 49 seeds in a bag? (iii) more that 35 seeds in a bag?

Solution: Total number of bags is 5. (i) Number of bags in which more than 40 seeds germinated out of50 seeds is 3. P(germination of more than 40 seeds in a bag) = 5/? = 0.6 (ii) Number of bags in which 49 seeds germinated = 0. P(germination of 49 seeds in a bag) = 0/5 = 0. (iii) Number of bags in which more than 35 seeds germinated = 5. So, the required probability =5/ 5 = 1.

Read More: Surface Area And Volume Of Combination Of Solids With Examples

• December,03 2021

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NCERT Solutions for Class 9 Maths Chapter 15 Probability

NCERT Solutions for Class 9 Maths Chapter 15 Probability is an article that contains all the resources for learning the solution to the problems given in the CBSE syllabus 2023-24. Using this NCERT Solutions, students can learn the methods for the solution of problems in a step-by-step manner. In NCERT Solutions for Class 9 Maths, all the problems given in the NCERT book for Class 9 Chapter 15 are solved. These Probability Class 9 NCERT Book Solutions are the perfect resource to help you master the chapter thoroughly.

Probability explores the idea of the likelihood that a particular experiment outcome will occur. Only one task, based on issues from real-world instances, is provided in this chapter to help the reader comprehend the experimental approach to probability . Events and the empirical formula for probability are some topics discussed in the article.

Class 9 Maths NCERT Solutions Chapter 15 Exercises
– 10 Questions (4 Short Answers, 3 Long Answers, 3 Very Long Answers)

Discover what’s covered in the solutions for Chapter 15 Maths Class 9

Exercises provided in the NCERT Solutions for Class 9 Maths Chapter 15 Probability

NCERT Solutions for Class 9 Maths Chapter 15, titled ‘Probability,’ delves into the concept of probability and its versatile applications across different domains. This chapter encompasses the following exercises:

NCERT Solutions for Class 9 Mathematics Chapter 15: Exercise 15.1

Question 1. in a cricket match, a bats-woman hits a boundary 6 times out of 30 balls she plays. find the probability that she did not hit a boundary..

Data given in the question:  Total number of balls batswoman plays = 30  Numbers of boundary hit by batswoman = 6  To find number of time batswoman didn’t hit boundary , we will subtract  ⇒(Total number of balls batswoman plays) – (Numbers of boundary hit by batswoman)  ⇒ 30 – 6 = 24  Probability of that she didn’t hit a boundary = 24/30 = 4/5

Question 2. 1500 families with 2 children were selected randomly, and the following data were recorded:

Compute the probability of a family, chosen at random, having

(i) 2 girls (ii) 1 girl (iii) no girl.

According to question  Total numbers of families given in the question 1500  (i) Numbers of families having 2 girls = 475  Probability of chosen 2 girls = Numbers of families having 2 girls / Total numbers of families  = 475/1500 = 19/60  Probability of chosen 2 girls is 19/60  (ii) Numbers of families having 1 girls = 814  Probability of chosen 1 girl = Numbers of families having 1 girl / Total numbers of families  = 814/1500 = 407/750  Probability of chosen 1 girl is 407/750  (iii) Numbers of families having 2 girls = 211  Probability of chosen 0 girl = Numbers of families having 0 girls/Total numbers of families  = 211/1500  Sum of the probability = (19/60)+(407/750)+(211/1500)  = (475+814+211)/1500  = 1500/1500 = 1  Yes, the sum of these probabilities is 1.

Question 3. Refer to Example 5, Section 14.4, Chapter 14. Find the probability that a student of the class was born in August.

According to questions:  Total number of students in the class in the given question = 40  Numbers of students born in August = 6  The probability that a student of the class was born in August = (Total numbers of students in the class) /  (Numbers of students born in August)  = 6/40 = 3/20

Question 4. Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up. 

Number of times 2 heads come up (in the given question) = 72  Total number of times the coins were tossed = 200  The probability of 2 heads coming up = (Number of times 2 heads come up) / (Total number of times the coins were tossed)  = 72/200 = 9/25

Question 5. An organisation selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. 

The information gathered is listed in the table below:.

Suppose a family is chosen. Find the probability that the family chosen is

(i) earning ₹10000 – 13000 per month and owning exactly 2 vehicles.

(ii) earning ₹16000 or more per month and owning exactly 1 vehicle.

(iii) earning less than ₹7000 per month and does not own any vehicle.

(iv) earning ₹13000 – 16000 per month and owning more than 2 vehicles.

(v) owning not more than 1 vehicle.  

Total number of families = 2400 (According to question)  (i) Numbers of families earning ₹10000 –13000 per month and owning exactly 2 vehicles = 29  The probability that the family chosen is earning ₹10000 – 13000 per month and owning exactly 2 vehicles =  (Numbers of families earning ₹10000 –13000 per month and owning exactly 2 vehicles) / (Total number of families)  = 29/2400  (ii) Number of families earning ₹16000 or more per month and owning exactly 1 vehicle = 579  The probability that the family chosen is earning ₹16000 or more per month and owning exactly 1 vehicle =  (Number of families earning ₹16000 or more per month and owning exactly 1 vehicle) / (Total number of families)  =579/2400  (iii) Number of families earning less than ₹7000 per month and does not own any vehicle = 10  The probability that the family chosen is earning less than ₹7000 per month and does not own any vehicle =  (Number of families earning less than ₹7000 per month and does not own any vehicle)/(Total number of families)  = 10/2400 = 1/240  (iv) Number of families earning ₹13000-16000 per month and owning more than 2 vehicles = 25  The probability that the family chosen is earning ₹13000 – 16000 per month and owning more than 2 vehicles =  (Number of families earning ₹13000-16000 per month and owning more than 2 vehicles ) / (Total number of families)  = 25/2400 = 1/96  (v) Number of families owning not more than 1 vehicle = 10+160+0+305+1+535+2+469+1+579 = 2062  The probability that the family chosen owns not more than 1 vehicle = 2062/2400 = 1031/1200

Question 6. Refer to Table 14.7, Chapter 14.

(i) Find the probability that a student obtained less than 20% in the mathematics test.

(ii) Find the probability that a student obtained marks 60 or above.

Total number of students = 90  (given in question)  (i) Number of students who obtained less than 20% in the mathematics test = 7  The probability that a student obtained less than 20% in the mathematics test =  ( Number of students who obtained less than 20% in the mathematics test)/(Total number of students)  = 7/90  (ii) Number of students who obtained marks 60 or above = 15+8 = 23  The probability that a student obtained marks 60 or above =  (Number of students who obtained marks 60 or above ) / (Total number of students)  = 23/90

Question 7. To know the opinion of the students about the subject statistics, a survey of 200 students was conducted.

The data is recorded in the following table.

Find the probability that a student chosen at random

(i) likes statistics, (ii) does not like it.

Total number of students = 135+65 = 200 (According to question)  (i) Number of students who like statistics = 135  The probability that a student likes statistics = (Number of students who like statistics) / (Total number of students)  = 135/200 = 27/40  (ii) Number of students who do not like statistics = 65  The probability that a student does not like statistics =  (Number of students who do not like statistics) / (Total number of students)  = 65/200 = 13/40

Question 8. Refer to Q.2, Exercise 14.2. What is the empirical probability that an engineer lives:

(i) less than 7 km from her place of work?

(ii) more than or equal to 7 km from her place of work?

(iii) Within ½ km from her place of work?

The distance (in km) of 40 engineers from their residence to their place of work were found as follows:  5 3 10 20 25 11 13 7 12 31 19 10 12 17 18 11 3 2  17 16 2 7 9 7 8 3 5 12 15 18 3 12 14 2 9 6  15 15 7 6 12  Total numbers of engineers = 40  (According to question)  (i) Number of engineers living less than 7 km from their place of work = 9  The probability that an engineer lives less than 7 km from her place of work =  (Number of engineers living less than 7 km from their place of work) / (Total numbers of engineers )  = 9/40  (ii) Number of engineers living more than or equal to 7 km from their place of work = 40-9 = 31  Probability that an engineer lives more than or equal to 7 km from her place of work =  (Number of engineers living more than or equal to 7 km from their place of work ) / (Total numbers of engineers)  = 31/40  (iii) Number of engineers living within ½ km from their place of work = 0  The probability that an engineer lives within ½ km from her place of work =  (Number of engineers living within ½ km from their place of work) / (Total numbers of engineers)  =0/40 = 0

Question 9. Activity: Note the frequency of two-wheelers, three-wheelers and four-wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two-wheeler.

The question is an activity to be performed by the students.

Question 10. Activity: Ask all the students in your class to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by 3? Remember that a number is divisible by 3, if the sum of its digits is divisible by 3.

Question 11. eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg):, 4.97      5.05      5.08     5.03     5.00     5.06     5.08      4.98       5.04       5.07       5.00, find the probability that any of these bags chosen at random contains more than 5 kg of flour..

Data given in the question  Total number of bags present = 11  Number of bags containing more than 5 kg of flour = 7  The probability that any of the bags chosen at random contains more than 5 kg of flour =  (Number of bags containing more than 5 kg of flour) / (Total number of bags present)  = 7/11

Question 12. In Q.5, Exercise 14.2, you were asked to prepare a frequency distribution table, regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12-0.16 on any of these days.

The data obtained for 30 days is as follows:.

0.03      0.08      0.08      0.09      0.04      0.17      0.16      0.05      0.02      0.06      0.18      0.20      0.11      0.08      0.12      0.13      0.22      0.07      0.08     0.01      0.10      0.06      0.09      0.18      0.11      0.07      0.05      0.07      0.01      0.04

Total number of days in which the data was recorded = 30 days (According to the question)  Numbers of days in which sulphur dioxide was present in between the interval 0.12-0.16 = 2  The probability of the concentration of sulphur dioxide in the interval 0.12-0.16 on any of these days =  (Numbers of days in which sulphur dioxide was present in between the interval 0.12-0.16) /  (Total number of days in which the data was recorded )  = 2/30 = 1/15

Question 13. In Q.1, Exercise 14.2, you were asked to prepare a frequency distribution table regarding the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group AB.

The blood groups of 30 students of class viii are recorded as follows:.

A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O.

Total numbers of students = 30 (according to questions)  Number of students having blood group AB = 3  The probability that a student of this class, selected at random, has blood group  AB = (Number of students having blood group AB) / (Total numbers of students)  = 3/30 = 1/10

Things to Keep in Mind Before Working on NCERT Class 9 Maths Chapter 15 – Probability

• All the solutions in the article are provided by the team of professionals at Gfg, which help users learn solutions with ease.
• These solutions are accurate and comprehensive in nature, which made them very simple and easy to understand.
• All the provided solutions are discussed in a step-by-step manner which helps students learn solutions with all of its intermediate steps.

Types of Questions Asked in Probability Class 9 Maths NCERT 

Here is a list of the different types of questions you’ll encounter in Chapter 15 of NCERT Maths for Class 9:

• Questions related to coins.
• Questions related to rolling dice.
• Questions involving a pack of cards.
• Questions related to the number system, like finding the probability of digits being even, odd, divisible by 3 or 4, etc.
• Questions about the occurrence of events.

Probability – Class 9 Math Chapter 15 NCERT Solutions Summary

Class 9 marks a significant transition for students as they step into the world of board exams. This can be both exciting and a bit daunting. The syllabus expands, introducing new and challenging subjects, especially mathematics, with unfamiliar concepts. Mastering these chapters and concepts is vital for building a strong foundation. The use of Class 9 Probability NCERT Solutions can greatly enhance your understanding, boosting your confidence as you progress to higher classes. These NCERT Solutions for Class 9 Probability serve as the building blocks of your knowledge, strengthening your educational base for future endeavors.

Also Check:

• NCERT Solutions for Class 9 English
• NCERT Solutions for Class 9 Biology
• NCERT Solutions for Class 9 English Beehive Chapter 1
• NCERT Solutions for Class 9 (2023-2024)
• NCERT Solutions for Class 8 to 12

FAQs on NCERT Solutions for Class 9 Maths Chapter 15-Probability

1. why is it important to learn probability.

It is crucial to understand probability because it supports decision-making, predictive modelling, risk assessment, scientific reasoning, and real-world scenarios. It offers a paradigm for comprehending ambiguity and making decisions that are well-informed.

2. What topics are covered in NCERT Solutions Class 9 Maths Probability?

NCERT Solutions for Class 9 Maths Chapter 15-Probability includes theory of probability and empirical probability.

3. How can NCERT Solutions for Class 9 Maths Chapter 15-Probability help me?

NCERT Solutions for Class 9 Maths Chapter 15-Probability can help you solve the NCERT exercise without any limitations. If you are stuck on a problem, you can find its solution in these solutions and free yourself from the frustration of being stuck on some question.

4. How many exercises are there in Class 9 Maths Chapter 15-Probability?

There are 1 exercises in the Class 9 Maths Chapter 15-Probability which covers all the important topics and sub-topics.

5. Where can I find NCERT Solutions for Class 9 Maths Chapter 15-Probability ?

You can find these NCERT Solutions in this article created by our team of experts at GeeksforGeeks.

6. Where can I find NCERT Solutions for Class 9 Maths Chapters?

you can Get chapter wise NCERT Solutions for Class 9 Maths prepared by experts. Visit GeeksforGeeks to get access to Class 9 Maths Solutions!

7. What are the Simple Ways to Solve the Questions?

The Class 9 Chapter 15 Maths NCERT Solutions provide straightforward answers to all the questions.

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Probability Class 9 Notes - Chapter 15

According to the CBSE Syllabus 2023-24, this chapter has been removed from  NCERT Class 9 Maths textbook .

CBSE Class 9 Maths Probability Notes:- Download PDF Here

Introduction to probability, probability.

• Probability is the measure of the likelihood of an event to occur. Events can’t be predicted with certainty but can be expressed as to how likely it can occur using the idea of probability.
• Probability can range between 0 and 1, where 0 probability means the event is an impossible one and probability of 1 indicates a certain event.

For more information On Probability, watch the below video

To know more about Probability, visit here .

An experiment

• Is any procedure that can be infinitely repeated or any series of actions that have a well-defined set of possible outcomes.
• Can either have only one or more than one possible outcome.
• Is also called the sample space.
• A single event that is performed to determine the outcome is called a trial.
• All possible trials that constitute a well-defined set of possible outcomes are collectively called an experiment/sample space.

Experimental Probability

Experimental/empirical probability.

The empirical probability of an event that may happen is given by:

Probability of event to happen P ( E ) =Number of favourable outcomes/Total number of outcomes

To know more about Experimental Probability, visit here .

Coin Tossing Experiment

Consider a fair coin. There are only two possible outcomes that are either getting heads or tails.

Number of possible outcomes = 2 Number of outcomes to get head = 1 The probability of getting head =Number of outcomes to get head/Number of possible outcomes=1/2

  Rolling of Dice Experiment

When a fair dice is rolled, the number that comes up top is a number between one to six. Assuming we roll the dice once, to check the possibility of three coming up.

Number of possible outcomes = 6 Number of outcomes to get three = 1 The probability of getting three = Number of outcomes to get three/Number of possible outcomes=1/6

Sum of Probabilities of Favorable and Unfavourable events

• When a trial is done for an expected outcome, there are chances when the expected outcome is achieved. Such a trial/event is called a favourable event.
• When a trial is done for an expected outcome, there are chances when the expected outcome is not achieved. Such a trial/event is called an unfavourable event.
• All favourable and unfavourable event outcomes come from a well-defined set of outcomes.
• Suppose an event of sample space S has n favourable outcomes. Then, there are S-n, unfavourable outcomes.
• The probability of favourable and unfavourable events happening depends upon the number of trials performed. However, the sum of both these probabilities is always equal to one.

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