Probability Class 11th Notes - Free NCERT Class 11 Maths Chapter 16 notes - Download PDF

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Probability Class 11th Notes - Free NCERT Class 11 Maths Chapter 16 notes - Download PDF

Edited By Ramraj Saini | Updated on Mar 22, 2022 05:49 PM IST

Class 11 Math chapter 16 notes are regarding Probability. In chapter 16 we will be going through the probability and outcomes concepts in Probability Class 11 notes. This Class 11 Maths chapter 16 notes contains the following topics: sample space, outcomes, events, types of events like simple, exclusive, exhaustive, exclusive, and exhaustive events, axiomatic approach, probability of an event, and Addition rule. NCERT Class 11 Math chapter 16 notes discuss probability using different theorems and addition, multiplication, and subtraction methods.

NCERT Class 11 Math chapter 16 notes have covered every topic from an exam point of view. NCERT notes for Class 11 Math chapter 16 textbook explains all the topics with examples that make them easy to understand. FAQ’s that are frequently asked questions by students collected from different places. CBSE Class 11 Maths chapter 16 notes help students to refer to them quickly to give a recap of all the topics with examples. Downloading them from Class 11 Maths chapter 16 notes pdf download, Probability Class 11 notes, Class 11 Probability notes pdf download.

Also, students can refer,

NCERT CLASS 11 CHAPTER 16 NOTES

Random Experiment:

To say it is a random experiment it must satisfy the following rules:

1. It has more than one outcome.

2. It’s outcomes cannot be predicted.

Outcomes:

The solution of the experiment is called outcome.

Sample Space:

The set of all possible chances or outcomes is called sample space.

Event:

Part of the sample space is called an event.

Events are of different types:

1. Impossible and sure events: The empty set Φ, sample space S are known to be the events. Φ is known as an impossible event and S, which is called the whole sample space, is called a sure event.

1. Simple Event: Each outcome that belongs to the sample space is called the simple or elementary event. An event with only one event or outcome is said to be a simple event.

1. Compound event: An event with more than one outcome is called a compound event.

1. Complementary events: If we have an event called A then we also have a complimentary event called A’ which denotes the complementary events.

1. Event A or B: If we consider either A or B events then they are represented as A∪B.

1. Event A and B: If we consider the intersection of A and B events then they are represented as A∩B.

1. Event A, not B: If we consider only A excluding the elements of B then we represent the events as A-B.

1. Mutually Exclusive Events: When we have two events named A and B, and if the intersection of the outcomes of the events A and B is “null” or Zero is called Mutually exclusive events. They are disjoint events. P(A∩B) = 0

1. Mutually exhaustive events: Let S be the sample space and the events of the space be E1, E2, E3,...................., En are said to be exhaustive events if E1 ∪ E2 ∪ E3 ∪………. ∪ En = S.

1. Mutually exclusive and exhaustive events: If Ei∩Ej= ∅ that is if they are disjoint and ∑Ei = S then the events are called mutually exclusive and exhaustive events.

Axiomatic Approach To Probability:

Let S be a sample space with probability P with the function f be a real-valued with domain S and range be in the interval of [0,1] should satisfy the axioms below:

1. P(E) ≥ 0 (or) 0 ≤ P(E) ≤ 1

2. P(S) =1 that is P(E1) + P(E2) + P(E3) +..........+P(N) =1

3. P(A) = ∑ P(wi) where wi is the elementary event.

Probability of An Event:

S be the sample space, E be the event, and n(s)= n and n(E)=m

Then the probability of the event= P(E)

Odd number of outcomes in favor of the event: m : (n-m)

Odd number of outcomes against the event : (n-m) : m

Probability of the event that does not occur or take place : P(A)= 1- P(A)

Probability of event A or B :

P(A∪B) = P(A) + P(B) - P(A∩B)

Probability of event A or B or C :

P(A∪B∪C) = P(A) + P(B) +P(C)-P(A∩B)-P(B∩C) - P(A∩C) + P(A∩B∩C)

If A, B are mutually exclusive events: Then P(A∪B) = P(A) + P(B)

Since A∩B in an exclusive event is zero or null.

With this topic we conclude NCERT Class 11 chapter 16 notes.

The link for NCERT textbook pdf is given below:

URL: ncert.nic.in/textbook/pdf/kemh116.pdf

Significance of NCERT Class 11 Maths Chapter 16 Notes:

NCERT Class 11 Maths chapter 16 notes will be very much helpful for students to score maximum marks in their 11 board exams. In Probability Class 11 chapter 16 notes we have discussed many topics: sample space, outcomes, events, types of events like simple, exclusive, exhaustive, exclusive, and exhaustive events, axiomatic approach, probability of an event, and Addition rule. NCERT Class 11 Maths chapter 16 is also very useful to cover major topics of Class 11 CBSE Maths Syllabus.

The CBSE Class 11 Maths chapter 16 is about finding the probability using different methods and theorems. FAQ’s most frequently asked questions regarding founder, real-life examples, applications, theorems are discussed. Probability Class 11 chapter 16 pdf download helps students in referring to it in a short span even before the exams as a quick review.

NCERT Class 11 Notes Chapter Wise.

 NCERT Class 11 Maths Chapter 1 Notes NCERT Class 11 Maths Chapter 2 Notes NCERT Class 11 Maths Chapter 3 Notes NCERT Class 11 Maths Chapter 4 Notes NCERT Class 11 Maths Chapter 5 Notes NCERT Class 11 Maths Chapter 6 Notes NCERT Class 11 Maths Chapter 7 Notes NCERT Class 11 Maths Chapter 8 Notes NCERT Class 11 Maths Chapter 9 Notes NCERT Class 11 Maths Chapter 10 Notes NCERT Class 11 Maths Chapter 11 Notes NCERT Class 11 Maths Chapter 12 Notes NCERT Class 11 Maths Chapter 13 Notes NCERT Class 11 Maths Chapter 14 Notes NCERT Class 11 Maths Chapter 15 Notes NCERT Class 11 Maths Chapter 16 Notes

NCERT Books and Syllabus

 NCERT Book for Class 11 NCERT Syllabus for Class 11

1. What are the applications of Probability Class 11 notes in real life?

Applications of probability in our real-life are:  sports, weather reports, blood samples, toss in a game, etc.

2. Few games in which probability NCERT Class 11 Math chapter 16 used?

Probability is used in the games like ludo, snake and ladder, cricket, playing cards, etc

3. Name of the Mathematicians who invented Probability Class 11 Math chapter 16 notes?

Blaise Pascal and Pierre de Fermat are the two french mathematicians who invented Probability.

4. Can the probability of an event be greater than 1 according to ncert class 11 maths chapter 16 notes?

No, it is always less than or equal to 1 but cannot be greater than 1.

5. What are the three basic rules used in probability NCERT notes for Class 11 Math chapter 16 and ncert notes for Class 11 Maths chapter 16?

Addition, multiplication, and complement are the three basic operations that we use in probability.

6. What is the range of probability of an event to occur in Class 11 Maths chapter 16 notes and notes for Class 11 Maths chapter 16?

The probability of an event can be from 0 to 1.

0 ≤ P(E) ≤ 1

It cannot be less than 0 or greater than 1.

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QA Manager

Quality Assurance Manager Job Description: A QA Manager is an administrative professional responsible for overseeing the activity of the QA department and staff. It involves developing, implementing and maintaining a system that is qualified and reliable for testing to meet specifications of products of organisations as well as development processes.

2 Jobs Available

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.

2 Jobs Available
Reliability Engineer

Are you searching for a Reliability Engineer job description? A Reliability Engineer is responsible for ensuring long lasting and high quality products. He or she ensures that materials, manufacturing equipment, components and processes are error free. A Reliability Engineer role comes with the responsibility of minimising risks and effectiveness of processes and equipment.

2 Jobs Available
Safety Manager

A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.

2 Jobs Available
Corporate Executive

Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.

2 Jobs Available
Computer Programmer

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.

3 Jobs Available
Product Manager

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.

3 Jobs Available
ITSM Manager

ITSM Manager is a professional responsible for heading the ITSM (Information Technology Service Management) or (Information Technology Infrastructure Library) processes. He or she ensures that operation management provides appropriate resource levels for problem resolutions. The ITSM Manager oversees the level of prioritisation for the problems, critical incidents, planned as well as proactive tasks.

3 Jobs Available
Information Security Manager

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

3 Jobs Available
Big Data Analytics Engineer

Big Data Analytics Engineer Job Description: A Big Data Analytics Engineer is responsible for collecting data from various sources. He or she has to sort the organised and chaotic data to find out patterns. The role of Big Data Engineer involves converting messy information into useful data that is clean, accurate and actionable.

2 Jobs Available
Cloud Solution Developer

A Cloud Solutions Developer is basically a Software Engineer with specialisation in cloud computing. He or she possesses a solid understanding of cloud systems including their operations, deployment with security and efficiency with no little downtime.

2 Jobs Available
CRM Technology Consultant

A Customer Relationship Management Technology Consultant or CRM Technology Consultant is responsible for monitoring and providing strategy for performance improvement with logged calls, performance metrics and revenue metrics. His or her role involves accessing data for team meetings, goal setting analytics as well as reporting to executives.

2 Jobs Available
IT Manager

Career as IT Manager  requires managing the various aspects of an organization's information technology systems. He or she is responsible for increasing productivity and solving problems related to software and hardware. While this role is typically one of the lower-level positions within an organisation, it comes with responsibilities related to people and ownership of systems.

2 Jobs Available