NCERT Solutions for Class 11 Maths Chapter 16 Probability (Ex 16.1) Exercise 16.1
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Mathematics is an important subject for pupils to learn in school. Strong mathematicalabilities can help students in many different ways throughout their lives. Moreover, Mathematics is essential for helping students comprehend the concepts presented in other subjects like Physics, Chemistry, etc. As a result, a strong foundation in Mathematics can enable pupils to succeed in other subjects as well. Numerous higher education courses continue the concepts covered in Class 11 as well. Many of the new concepts that are introduced to students in Class 11 are used in higherlevel courses of study. For students who intend to study Mathematics in college, the concepts taught in Class 11 are very important. Therefore, pupils would benefit in various ways from having a strong understanding of Mathematics in Class 11 in addition to helping them get good exam results. Many students find the concepts in Class 11 interesting to learn. However, achieving high results in the annual exams requires more than just reading. The very foundation of Mathematics is practice. It takes a lot of effort to score good grades in Mathematics. According to experts, pupils should finish the NCERT exercises in order to fully understand the chapters.However, the exercises’ questions are not simple to answer. Some questions are extremely difficult to answer and have a tendency to baffle students. As a result, they search for the answers to the exercises’ questions. Finding NCERT solutions, however, is difficult, particularly for Class 11 students. Additionally, even if it is available, it needs to be written in an easily understandable manner so that students can understand it. As a result, Extramarks offers NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1.
Students must use the books produced by the National Council of Educational Research and Training in accordance with CBSE norms. The Mathematics textbooks for Class 12 are published by the NCERT. There are 16 chapters in the Class 11 NCERT Mathematics textbook. The NCERT books should be read by students preparing for the annual exams. Students should try to answer the book’s questions after finishing each chapter, including those in the examples and exercises. Students need the answers to the questions in order to evaluate their answers. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 is therefore available from Extramarks. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 is therefore available from Extramarks. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 have been provided by Extramarks in a stepbystep approach to help Class 11 students fully comprehend the problems, even if they are tackling them for the first time. Alternative solutions to some questions that are easier to understand are also included in Extramarks’ NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1.
The problems in the exercises in the NCERT books have answers. However, only providing answers is insufficientsince students also need to learn the methods required to arrive at the answer. If the methods and steps are clear, students can learn how to respond to any question that is posed to them. Extramarks’ NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.1 is an example of a study resource that allows students to comprehend and learn about the solutions and methods from the ground up.
In addition to the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1, Extramarks also provides various study materials for students in Class 11. The study materials make it easier to fully comprehend the ideas required to do Exercise 16.1 Class 11 Maths. This study material also helps pupils revise their chapters. It was created by highly qualified academics with many years of expertise in a clear and understandable way. Extramarks provides practise worksheets for each chapter, MCQs, solved exemplar problems, sample question papers, and more. As a result, students do not have to search elsewhere for more materials because they can find everything they need in one place. Students can study with some of India’s top instructors through Extramarks, who have years of professional expertise in their respective disciplines. They thoroughly explain each topic using learning modules with rich media. As a tool to assist students maximise their scores and accomplish their learning objectives, Extramarks focuses on building concepts. To help students with their preparation, subject experts have also provided numerous other resources, including the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 and others.
For competitive exams like JEE Main and JEE Advanced as well as the CBSE board exams, the chapter on Probability is very crucial. Students’ achievement on these exams influences their careers because college admissions are determined by them. They experience tension and, occasionally, mental exhaustion as a result of the tremendous burden that is put on them. Students can help themselves grasp and retain the concepts by properly practising the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 and the other study materials offered on Extramarks. Students studying for entrance exams like the JEE Main can also get study materials and practise tests from Extramarks. For a quick study before exams, students can use the sample questions and brief revision notes. As they get ready for several tests, this will give them more confidence.
Before exams, students need access to a range of questions as well as clearly explained solutions.The majority of question banks base their questions on NCERT textbook problems.When students have access to the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1, answering questions is easier. They pick up on the concepts more quickly as a result. One feels more prepared for any exam when one learns and understands concepts rapidly.Furthermore, this allows them to study for longer periods of time while maintaining mental focus on other aspects of their learning.By understanding the methods outlined in the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1, students can advance in their preparation. Having access to the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 that are tailored to students’ needs can be a useful study tool, despite the chapter’s occasionally challenging and complex content. Utilizing these learning materials can make studying Probability an easier task. Students can practise by completing the NCERT questions if they want to progress continuously while finishing other papers or problems. Extramarks’ NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.1 focuses on a specific chapter.There are several learning modules and a wide range of study resources available to students who desire to perform better in their annual exams, including chapterbychapter worksheets and sample tests. As a result, Extramarks serves as a onestop destination for testing, practice, and study. The fact that Extramarks’ NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 are created and curated by skilled subject professionals guarantees a flawless learning experience for all students.
NCERT Solutions for Class 11 Maths Chapter 16 Probability (Ex 16.1) Exercise 16.1
Extramarks provides a complete approach to a student’s educational needs. Despite the fact that NCERT textbooks are an excellent source of study material, students often struggle to find trustworthy NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.1.Although the NCERT textbook contains the answers to the questions, it does not contain their indepth explanations. Students must comprehend the steps taken to arrive at the answer while answering the questions. Writing every step in the exam is extremely crucial to getting full marks. Extramarks provides authentic and thorough NCERT solutions. Further, it gives students a seamless learning experience by combining the advantages of realworld classrooms and the Learning App. Finding the NCERT solutions is particularly challenging for students who face internet connectivity issues. It is possible that pupils will not always have access to the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1. Students who want to continue their studies should have a PDF copy of the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 on hand. Each and every student’s educational demands are fully met by Extramarks. Although NCERT textbooks make excellent study resources, students still have trouble finding dependable NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1. Extramarks offers accurate and comprehensive NCERT solutions. The Extramarks website and mobile app both offer the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 in PDF format. Additionally, it is simple for students to download the PDF version and answer the questions whenever they like. By combining the benefits of live classrooms with learning apps in one comprehensive learning package, it also provides students with a seamless learning experience.
Access NCERT Solutions for Class 11 Maths Chapter 16 Probability
NCERT solutions can be found all over the internet. There are many websites that provide expertly prepared NCERT solutions for students in Class 11. However, students need to be sure that these sources are reliable. Every learning platform is not reliable. Only a select few platforms that offer NCERT solutions from knowledgeable and experienced teachers are useful for pupils. Extramarks is an example of such a platform. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 in PDF format, might not always be available to students. At Extramarks, students can access reliable NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1.
Exercise 16.1
Exercise 16.1 contains 16 questions. These questions are based on the outcomes and sample space of an experiment. Some of the questions in the exercises can be confusing for the students. Students preparing for their yearly exams can benefit from the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 since they are prepared in simple language that all students can understand. In order to help students earn full marks on their exams, the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 have been created in a stepwise manner. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 are developed in accordance with the most recent syllabus to avoid causing students to go elsewhere for the topics covered by the curriculum. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 comply with all CBSE guidelines. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 cover every question in the Class 11th Maths Chapter 16 Exercise 16.1 and are also completely errorfree. Students can get ready for exams by using the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 to assist them in quickly and accurately responding to questions like these. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 provided by Extramarks will be sufficient to help the students in answering the NCERT problems because they were written in an easytounderstand manner. Students can apply the ideas from Class 11 Maths Exercise 16.1 more precisely and conveniently by using the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1.
NCERT Solutions for Class 11 Maths Chapter 16 Probability Exercise 16.1
Receiving the proper instruction is crucial for understanding the numerous concepts covered in the Class 11 Mathematics curriculum. Success in subjects like Mathematics can be challenging, and the pressure of multiple exams only makes it more challenging. In addition to utilising various types of help, students can also get NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 prepared by top subject experts to gain a complete understanding of the principles in a certain topic. Through the meticulously crafted learning resources offered by Extramarks, students can receive the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 from distinguished subject experts. Students can gain confidence in their study plan and upcoming tests with the help of subject experts.Class 11 comprises a variety of tests and examinations at the school level to help students further their education. However, students need guidance from experienced professionals in order to perform well in their exams. Having the opportunity to obtain NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 from top subject specialists may help with exam preparation.
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The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 provide complete, errorfree answers to all the exercise’s questions. Students can answer such problems fast and accurately in the exams by repeatedly practising the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1. Students can more correctly apply the ideas covered in the chapter by using the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1. The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 have been properly produced by highly qualified experts. The amount of knowledge that pupils in Class 11 have kept in mind to produce these solutions. The problems in this exercise have been done stepwise to make it easier to write answers in tests, as examiners always emphasise writing stepbystep answers in exams. The stepwise answers in the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 help students get maximum marks on tests. The large number of formulas provided in the NCERT textbook can be confusing for many students to understand and memorise, preventing them from using the formulas to solve the problems in the exercises. When students practise the stepbystep solutions in the NCERT Solutions for Class 11 Maths Chapter 16 Exercise 16.1, the formulas become easier to remember and apply.
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Q.1 In each of the following Exercises 1 to 7, describe the sample space for the indicated experiment.
1. A coin is tossed three times.
2. A die is thrown two times.
3. A coin is tossed four times.
4. A coin is tossed and a die is thrown.
5. A coin is tossed and then a die is rolled only in case a head is shown on the coin.
6. 2 boys and 2 girls are in Room X, and 1 boy and 3 girls in Room Y. Specify the sample space for the experiment in which a room is selected and then a person.
7. One die of red colour, one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Describe the sample space.
Ans.
1. Sample space for a coin tossed three times is:
{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
2. Sample space for a die thrown two times is:
{(x, y): x, y=1, 2, 3, 4, 5, 6} In other ways:
$\left\{\begin{array}{l}(1,\text{}1),\text{}(1,\text{}2),\text{}(1,\text{}3),\text{}(1,\text{}4),\text{}(1,\text{}5),\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}(1,\text{}6)\\ (2,\text{}1),\text{}(2,\text{}2),\text{}(2,\text{}3),\text{}(2,\text{}4),\text{}(2,\text{}5),\text{}(2,\text{}6)\\ (3,\text{}1),\text{}(3,\text{}2),\text{}(3,\text{}3),\text{}(3,\text{}4),\text{}(3,\text{}5),\text{\hspace{0.17em}\hspace{0.17em}}(3,\text{}6)\\ (4,\text{}1),\text{}(4,\text{}2),\text{}(4,\text{}3),\text{}(4,\text{}4),\text{}(4,\text{}5),\text{\hspace{0.17em}\hspace{0.17em}}(4,\text{}6)\\ (5,\text{}1),\text{}(5,\text{}2),\text{}(5,\text{}3),\text{}(5,\text{}4),\text{}(5,\text{}5),\text{\hspace{0.17em}\hspace{0.17em}}(5,\text{}6)\\ (6,\text{}1),\text{}(6,\text{}2),\text{}(6,\text{}3),\text{}(6,\text{}4),\text{}(6,\text{}5),\text{\hspace{0.17em}\hspace{0.17em}}(6,\text{}6)\end{array}\right\}$
3. Sample space for a coin tossed four times is:
$\left\{\begin{array}{l}\mathrm{HHHH},\mathrm{HHHT},\mathrm{HHTH},\mathrm{HTHH},\mathrm{THHH},\mathrm{HHTT},\mathrm{HTTH},\mathrm{HTHT},\\ \mathrm{THHT},\mathrm{THTH},\mathrm{TTHH},\mathrm{TTTH},\mathrm{HTTT},\mathrm{TTHT},\mathrm{THTT},\mathrm{TTTT}\text{}\end{array}\right\}$
4. Sample space for a tossed coin thrown die is:
$\{\mathrm{H}\text{\hspace{0.17em}}1,\mathrm{H}\text{\hspace{0.17em}}2,\mathrm{H}\text{\hspace{0.17em}}3,\mathrm{H}\text{\hspace{0.17em}}4,\mathrm{H}5,\mathrm{H}\text{\hspace{0.17em}}6,\mathrm{T}1,\mathrm{T}2,\mathrm{T}3,\mathrm{T}4,\mathrm{T}5,\mathrm{T}6\}$
5. Sample space when a coin is tossed and then a die is rolled only when head is shown on the coin:
$\{\mathrm{H}\text{\hspace{0.17em}}1,\mathrm{H}\text{\hspace{0.17em}}2,\mathrm{H}\text{\hspace{0.17em}}3,\mathrm{H}\text{\hspace{0.17em}}4,\mathrm{H}5,\mathrm{H}\text{\hspace{0.17em}}6,\mathrm{T}\}$
6. The sample space for the experiment in which a room is selected and then a person is:
$\{{\mathrm{XB}}_{1},{\mathrm{XB}}_{2},{\mathrm{XG}}_{1},{\mathrm{XG}}_{2},{\mathrm{YB}}_{3},{\mathrm{YG}}_{3},{\mathrm{YG}}_{4},{\mathrm{YG}}_{5}\}$
7. Dice in red colour, white colour and blue colour are shown by R, W and B respectively. Then the required sample space is
$\{\mathrm{R}1,\mathrm{R}2,\mathrm{R}3,\mathrm{R}4,\mathrm{R}5,\mathrm{R}6,\mathrm{W}1,\mathrm{W}2,\mathrm{W}3,\mathrm{W}4,\mathrm{W}5,\mathrm{W}6,\mathrm{B}1,\mathrm{B}2,\mathrm{B}3,\mathrm{B}4,\mathrm{B}5,\mathrm{B}6\}$
Q.2 An experiment consists of recording boy–girl composition of families with 2 children.
(i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?
(ii) What is the sample space if we are interested in the number of girls in the family?
Ans.
The boy and girl are represented by B and G respectively.
(i) The required sample space is:
{ BB,BG,GB,GG }
(ii) Sample space according to number of children in family is:
{ 0, 1, 2 }
Q.3 A box contains 1 red and 3 identical white balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.
Ans.
A red ball and white ball are represented by R and W respectively.
The required sample space is:
{ RW, WR, WW }.
Q.4 An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.
Ans.
The head and tail are represented by H and T respectively.
The required sample space, when coin and die is thrown according to given condition, is:
{ HH, HT, T1, T2, T3, T4, T5, T6 }
Q.5 Suppose 3 bulbs are selected at random from a lot. Each bulb is tested and classified as defective (D) or non – defective(N). Write the sample space of this experiment.
Ans.
The required sample space is:
{DDD, DDN, DND, NDD, DNN, NDN, NND, NNN}
Q.6 A coin is tossed. If the outcome is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for the experiment?
Ans.
Sample space according to given conditions is:
{ T, H1, H3, H5, H21, H22, H23, H24, H25, H26, H41, H42, H43, H44, H45, H46, H61, H62, H63, H64, H65, H66 }
Q.7 The numbers 1, 2, 3 and 4 are written separatly on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the sample space for the experiment.
Ans.
The required sample space is:
{(1, 2), (1, 3), (1, 4), (2, 1), (2, 3), (2, 4), (3, 1), (3, 2), (3, 4), (4, 1), (4, 2), (4, 3)}
Q.8 An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.
Ans.
The required sample space is:
{1HH, 1HT, 1TH, 1TT, 2H, 2T, 3HH, 3HT, 3TH, 3TT, 4H, 4T, 5HH, 5HT, 5TH, 5TT, 6H, 6T }
Q.9 A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.
Ans.
The required sample space is:
{TR_{1}, TR_{2}, TB_{1}, TB_{2}, TB_{3}, H1, H2, H3, H4, H5, H6}
Q.10 A die is thrown repeatedly until a six comes up. What is the sample space for this experiment?
Ans.
Sample space when a die is thrown until a six is obtained.
{ 6, (1, 6), (2,6), (3,6), (4,6), (5,6), (1, 1, 6), (1, 2, 6), (1, 3, 6), (1, 4, 6), (1, 5, 6), (2,1,6), (2, 2, 6),…, (2,5,6), (3,1,6), (3, 2, 6), (3,3,6), (3, 4, 6), (3, 5, 6) …}
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FAQs (Frequently Asked Questions)
1. How many questions have been solved in the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1?
All the 16 questions have been solved in the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 provided by Extramarks.
2. Where to find the NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1?
The NCERT Solutions For Class 11 Maths Chapter 16 Exercise 16.1 are available on the Extramarks website and mobile app.