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In this article, you will get Class 11 Maths chapter 16 miscellaneous exercise solutions. As the name suggests the miscellaneous exercise chapter 16 Class 11 consist of mixed questions from all the topics covered in this chapter. There are many questions related to finding the probability of an event, probability of the complement of an event in the NCERT book miscellaneous exercise chapter 16 Class 11. Also, you will get questions related to finding the probability of mutually exclusive events, exhaustive and equally likely outcomes in the NCERT solutions for Class 11 Maths chapter 16 miscellaneous exercise.
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You can try to solve these NCERT syllabus problems which will check the conceptual understanding of this chapter. As miscellaneous exercise chapter 16 Class 11 is considered to be a bit difficult as compared to other exercises of this chapter you may find the difficulties while solving them. You can go through these Class 11 Maths chapter 16 miscellaneous solutions to get conceptual clarity.
These class 11 chapter 16 maths miscellaneous solutions are curated by subject experts at Careers360 in easy-to-understand language, explaining each step in detail. PDF versions of the class 11 maths ch 16 miscellaneous exercise solutions are also available, allowing students to access them anytime, anywhere at no cost. Also, check NCERT Solutions, If you are looking for NCERT solutions for Class 6 to Class 12 at one place.
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**According to the CBSE Syllabus for the academic year 2023-24, this chapter has been renumbered as Chapter 14.
Answer:
Given,
No. of red marbles = 10
No. of blue marbles = 20
No. of green marbles = 30
Total number of marbles = 10 + 20 + 30 = 60
Number of ways of drawing 5 marbles from 60 marbles =
(i) .
Number of ways of drawing 5 blue marbles from 20 blue marbles =
Probability of drawing all blue marbles =
Answer:
Given,
No. of red marbles = 10
No. of blue marbles = 20
No. of green marbles = 30
Total number of marbles = 10 + 20 + 30 = 60
Number of ways of drawing 5 marbles from 60 marbles =
(ii). We know,
The probability that at least one marble is green = 1 - Probability that no marble is green
Now, Number of ways of drawing no green marbles = Number of ways of drawing only red and blue marbles
=
The probability that no marble is green =
The probability that at least one marble is green =
Answer:
Total number of ways of drawing 4 cards from a deck of 52 cards =
We know that there are 13 diamonds and 13 spades in a deck.
Now, Number of ways of drawing 3 diamonds and 1 spade =
Probability of obtaining 3 diamonds and 1 spade
Answer:
Total number of faces of a die = 6
(i) Number of faces with number '2' = 3
Therefore, required probability P(2) is 0.5
Question:3.(ii) A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine
P(1 or 3)
Answer:
Total number of faces of a die = 6
(ii) P (1 or 3) = P (not 2) = 1 − P (2)
Therefore, required probability P(1 or 3) is 0.5
Question:3.(iii) A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine
P(not 3)
Answer:
Total number of faces of a die = 6
(iii) Number of faces with number '3' = 1
P(not 3) = 1 - P(3)
Therefore, required probability P(not 3) is
Answer:
Given, Total number of tickets sold = 10,000
Number of prizes awarded = 10
(a) If one ticket is bought,
P(getting a prize) =
P(not getting a prize) = 1 - P(getting a prize)
Answer:
Given, Total number of tickets sold = 10,000
Number of prizes awarded = 10
(b) If two tickets are bought:
Number of tickets not awarded = 10000 - 10 = 9990
P(not getting a prize) =
Answer:
Given, Total number of tickets sold = 10,000
Number of prizes awarded = 10
(c) If ten tickets are bought:
Number of tickets not awarded = 10000 - 10 = 9990
P(not getting a prize) =
Question:5.(a) Out of students, two sections of and are formed. If you and your friend are among the students, what is the probability that
you both enter the same section?
Answer:
Total number of students = 100
Let A and B be the two sections consisting of 40 and 60 students respectively.
Number of ways of selecting 2 students out of 100 students.=
If both are in section A:
Number of ways of selecting 40 students out of 100 = (The remaining 60 will automatically be in section B!)
Remaining 38 students are to be chosen out of (100-2 =) 98 students
Required probability if they both are in section A =
Similarly,
If both are in section B:
Number of ways of selecting 60 students out of 100 = (The remaining 40 will automatically be in section A!)
Remaining 58 students are to be chosen out of (100-2 =) 98 students
Required probability if they both are in section B =
Required probability that both are in same section = Probability that both are in section A + Probability that both are in section B
=
Hence, the required probability that both are in same section is
Question:5.(b) Out of students, two sections of and are formed. If you and your friend are among the students, what is the probability that
you both enter the different sections?
Answer:
Total number of students = 100
Let A and B be the two sections consisting of 40 and 60 students respectively.
We found out in (a) that the probability that both students are in same section is
(b) Probability that both the students are in different section =
Answer:
Given, 3 letters are put in 3 envelopes.
The number of ways of putting the 3 different letters randomly = 3!
Number of ways that at least one of the 3 letters is in the correct envelope
= No. of ways that exactly 1 letter is in correct envelope + No. of ways that 2 letters are in the correct envelope(The third is automatically placed correctly)
= No. of ways that exactly 1 letter is in correct envelope + No. of ways that all the 3 letters are in the correct envelope
=
(Explanation for :
No. of ways of selecting 1 envelope out of 3 = .
If we put the correct letter in it, there is only one way the other two are put in the wrong envelope! )
Therefore, the probability that at least one letter is in its proper envelope =
Question:7(i) A and B are two events such that , and Find
Answer:
Given, P(A) = 0.54, P(B) = 0.69, P(A B) = 0.35
(i) We know, P(A B) = P(A) + P(B) - P(A B)
P(A B) = 0.54 + 0.69 - 0.35 = 0.88
P(A B) = 0.88
Question:7(ii) A and B are two events such that , and . Find
Answer:
Given,
And,
(ii) [De Morgan’s law]
So,
Question:7(iii) A and B are two events such that , and Find
Answer:
Given, P(A) = 0.54, P(B) = 0.69, P(A B) = 0.35
And, P(A B) = 0.88
(iii) P(A B') = P(A-B) = P(A) - P(A B)
= 0.54 - 0.35 = 0.19
P(A B') = 0.19
Question:7(iv) A and B are two events such that , and . Find
Answer:
Given, P(A) = 0.54, P(B) = 0.69, P(A B) = 0.35
And, P(A B) = 0.88
(iv) P(B A') = P(B-A) = P(B) - P(A B)
= 0.69 - 0.35 = 0.34
P(B A') = 0.34
S. No. | Name | Sex | Age in years |
1. | Harish | M | 30 |
2. | Rohan | M | 33 |
3. | Sheetal | F | 46 |
4. | Alis | F | 28 |
5. | Salim | M | 41 |
A person is selected at random from this group to act as a spokesperson. What is the probability that the spokesperson will be either male or over years?
Answer:
Given,
Total number of persons = 5
No. of male spokesperson = 3
No. of spokesperson who is over 35 years of age = 2
Let E be the event that the spokesperson is a male and F be the event that the spokesperson is over 35 years of age.
Since only one male is over 35 years of age,
We know,
Therefore, the probability that the spokesperson will either be a male or over 35 years of age is .
Answer:
Since 4-digit numbers greater than 5000 are to be formed,
The place digit can be filled up by either 7 or 5 in ways
Since repetition is allowed,
Each of the remaining 3 places can be filled by any of the digits 0, 1, 3, 5, or 7 in ways.
Total number of 4-digit numbers greater than 5000 =
(5000 cannot be counted, hence one less)
We know, a number is divisible by 5 if unit’s place digit is either 0 or 5.
Total number of 4-digit numbers greater than 5000 that are divisible by 5 =
Therefore, the required probability =
Answer:
Since 4-digit numbers greater than 5000 are to be formed,
The place digit can be filled up by either 7 or 5 in ways
Since repetition is not allowed,
The remaining 3 places can be filled by remaining 4 digits in ways.
Total number of 4-digit numbers greater than 5000 =
We know, a number is divisible by 5 if unit’s place digit is either 0 or 5.
Case 1. When digit at place is 5, the units place can be filled only with 0.
And the & places can be filled with any two of the remaining digits {1,3,7} in
Number of 4-digit numbers starting with 5 and divisible by 5 =
Case 2. When digit at place is 7, the units place can be filled by 0 or 5 in 2 ways.
And the & places can be filled with any two of the remaining 3 digits in
Number of 4-digit numbers starting with 7 and divisible by 5 =
Total number of 4-digit numbers greater than 5000 that are divisible by 5 = 6 + 12 = 18
Therefore, the required probability =
Answer:
Given, Each wheel can be labelled with 10 digits.
Number of ways of selecting 4 different digits out of the 10 digits =
These 4 digits can arranged among themselves is ways.
Number of four digit numbers without repetitions =
Number of combination that can open the suitcase = 1
Required probability of getting the right sequence to open the suitcase =
In the Class 11 Maths chapter 16 miscellaneous exercise solutions there are 10 questions from topics of all the previous exercises of this chapter. There are some solved examples given before the miscellaneous exercise chapter 16 Class 11. You can start with solving these examples which will make it easy to solve exercise problems by yourself.
Also Read| Probability Class 11 Notes
Comprehensive Coverage: The miscellaneous exercise class 11 chapter 16 cover a wide range of miscellaneous problems, ensuring a thorough understanding of diverse mathematical concepts.
Clarity in Explanation: Subject experts provide clear and concise explanations for each problem, making it easy for students to comprehend the class 11 chapter 16 maths miscellaneous solutions.
Step-by-Step Approach: Class 11 maths miscellaneous exercise chapter 16 solutions are presented in a step-by-step format, helping students follow the logical progression of solving mathematical problems.
Application of Formulas: The class 11 maths ch 16 miscellaneous exercise solutions showcase the proper application of relevant formulas, aiding students in mastering the mathematical techniques required for problem-solving.
Practice Questions: The miscellaneous solutions include a variety of practice questions, offering students ample opportunities to reinforce their understanding of the chapter.
Accessible Language: Written in accessible language, the solutions cater to a broad audience, ensuring that students can easily grasp the concepts presented.
Digital and Printable Formats: The class 11 chapter 16 miscellaneous exercise solutions are available in digital formats, and students also have the option to download and print them, providing flexibility in study preferences.
Alignment with CBSE Syllabus: The solutions are aligned with the Class 11 CBSE syllabus, ensuring relevance and suitability for exam preparation.
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Happy learning!!!
Sample space this experiment = { HH, HT, TH, TT}
Probability of both head = 1/4
Sample space this experiment = { HH, HT, TH, TT}
Probability of at least one head = 3/4
Sample space = { 1, 2, 3, 4, 5, 6}
The probability of getting a number less than or equal to 3 = 1/2
Here you will get Syllabus for CBSE Class 11.
Check here for Syllabus for CBSE Class 11 Maths.
Calculus has 5 marks weightage in the CBSE Class 11 Maths.
statistics and probability have 10 marks weightage in the CBSE Class 11 Maths.
Mathematical Reasoning has 2 marks weightage in the CBSE Class 11 Maths.
The field of biomedical engineering opens up a universe of expert chances. An Individual in the biomedical engineering career path work in the field of engineering as well as medicine, in order to find out solutions to common problems of the two fields. The biomedical engineering job opportunities are to collaborate with doctors and researchers to develop medical systems, equipment, or devices that can solve clinical problems. Here we will be discussing jobs after biomedical engineering, how to get a job in biomedical engineering, biomedical engineering scope, and salary.
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Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.
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A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.
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Linguistic meaning is related to language or Linguistics which is the study of languages. A career as a linguistic meaning, a profession that is based on the scientific study of language, and it's a very broad field with many specialities. Famous linguists work in academia, researching and teaching different areas of language, such as phonetics (sounds), syntax (word order) and semantics (meaning).
Other researchers focus on specialities like computational linguistics, which seeks to better match human and computer language capacities, or applied linguistics, which is concerned with improving language education. Still, others work as language experts for the government, advertising companies, dictionary publishers and various other private enterprises. Some might work from home as freelance linguists. Philologist, phonologist, and dialectician are some of Linguist synonym. Linguists can study French, German, Italian.
The career of a travel journalist is full of passion, excitement and responsibility. Journalism as a career could be challenging at times, but if you're someone who has been genuinely enthusiastic about all this, then it is the best decision for you. Travel journalism jobs are all about insightful, artfully written, informative narratives designed to cover the travel industry. Travel Journalist is someone who explores, gathers and presents information as a news article.
Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.
A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.
A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.
A metallurgical engineer is a professional who studies and produces materials that bring power to our world. He or she extracts metals from ores and rocks and transforms them into alloys, high-purity metals and other materials used in developing infrastructure, transportation and healthcare equipment.
An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems.
An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.
Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.
A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.
Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack