NCERT Solutions Class 12 Mathematics Chapter 13 – Probability
The Class 12 Mathematics textbook has a total of 13 essential chapters. The last chapter 13 is about ‘Probability’ which continues after the ‘Linear Programming’ section. With NCERT Solutions Class 12 Mathematics Chapter 13, students will learn about Probability in detail. Extramarks notes are easy to understand as the subject experts ensure that solutions are given in the simplest form. These solutions include all the exercise questions covered in the book and harmonise with the new update on the CBSE syllabus.
Students can also utilise the solutions for Class 12 Mathematics chapter 13 to practise at their liberty. Students will get to learn the basic principles of Probability and get a strong base when they refer to our NCERT Solutions Class 12 Mathematics Chapter 13 for solutions. Our chapters are prepared by Extramarks experts who have tried to explain this topic in as simple terms as possible.
Probability is a core subject of Mathematics that deals with the occurrence of a random incident. Probability has been presented in Mathematics to foresee how likely events are to happen. This is the basic Probability theory, which is also applied in the Probability distribution, where you will learn the possibilities of the outcomes for a random observation.
NCERT Solutions Class 12 help students judge the accuracy of an event by analysing seemingly persuasive data. This gives students a solid introduction to Probability Mathematics while studying both advantages and limitations of applying Probability theory to different situations under varied conditions.
Key Topics Covered In NCERT Class 12 Mathematics Chapter 13
Probability is the measure of the chance of an event to occur. Most of the events cannot be predicted with total certainty, but we can expect the likelihood of an incident that is about to happen. Probability can range from 0 to 1, where 0 means that the situation would be impossible, and 1 specifies a particular event.
The important topics discussed in NCERT Solutions for Class 12 Mathematics Chapter 13 – Probability are:
| Exercise |
Topic |
| 13.1 |
Introduction |
| 13.2 |
Conditional Probability |
| 13.3 |
Multiplication Theorem on Probability |
| 13.4 |
Independent Events |
| 13.5 |
Bayes’ Theorem |
| 13.6 |
Random Variables and its Probability Distributions |
| 13.7 |
Bernoulli Trials and Binomial Distribution |
13.1 Introduction
The Probability formula has been defined as the possibility of an event to occur. The formula for an incident’s possibility is P(E) = Number of favourable outcomes / Total number of outcomes. This is equal to the ratio of promising results and the total number of outcomes. NCERT Solutions Class 12 Mathematics Chapter 13 provides detailed theory and practical solutions to Probability Mathematics.
13.2 Conditional Probability
Conditional Probability is the feasibility of an incident or outcome occurring based on the happening of the previous event or outcome. This can consider any event that has already taken place in the past. NCERT Solutions Class 12 Mathematics Chapter 13 takes you through all the calculations necessary in conditional Probability. Also, the properties of conditional Probability are one or two current independent events and a set of prior incidents.
13.3 Multiplication Theorem on Probability
According to the Probability multiplication rule, the likelihood of two occurrences of both the events A and B is equal to the product of the Probability of B occurring and the conditional Probability that event A happens while simultaneously event B occurs. The outcome of their distinct possibilities represents the Probability of simultaneous occurrences of two self-determining incidents. NCERT Solutions Class 12 Mathematics Chapter 13 clarifies the Theorem with practical examples.
13.4 Independent Events
The events are independent if the occurrence is not dependent on any other event, or the change in any one event doesn’t result in any change in the occurrence of another event. The events are mutually independent of each other. NCERT Solutions Class 12 Mathematics Chapter 13 lets you learn the definition of separate events in Probability and different diagrams and examples. There are various types of events such as mutually exclusive events, dependent events and independent events.
13.5 Bayes’ Theorem
Bayes’ Theorem describes the Probability of occurrence of an incident related to any condition. The formula for the possibility of causes is known as Bayes’ Theorem. You can learn about Bayes’ Theorem, its formula, derivation and solved examples in NCERT Solutions Class 12 Mathematics Chapter 13 by Extramarks. The Probability of occurrences of an incident calculated depending on other conditions is also called conditional Probability. Bayes’ Theorem can be obtained for events and random variables separately, implementing the definition of conditional Probability and density.
13.6 Random Variables and their Probability Distributions
Random Variables and its Probability Distributions is a real-valued function whose domain is the sample space of the random experiment. That means each outcome of a random experiment is related to a single real number, and a single real number may vary with the varied results of a random experiment. You can go through the example experiments provided in NCERT Solutions Class 12 Mathematics Chapter 13 to understand these distributions better. There are mean, variance and standard deviation of random variables.
13.7 Bernoulli Trials and Binomial Distribution
Bernoulli distribution is the Probability distribution for a series of Bernoulli trials with only two possible results. Bernoulli Trials are also called a binomial distribution. In a binomial distribution, we obtain a number of successes in a series of independent experiments, but in Bernoulli trials, we have only two possible outcomes. With NCERT Solutions Class 12 Mathematics Chapter 13, you can learn about Bernoulli distribution, its properties, Bernoulli trial formula, and the relationship between Bernoulli trials and binomial distribution.
Access NCERT Solutions Class 12 Mathematics Chapter 13 Exercises & Answer Solutions
The exercise and solutions paper are available on the Extramarks website. These questions will help students clear all doubts and understand the concept better to solve the Mathematical problems. NCERT Solutions Class 12 Mathematics Chapter 13 includes questions according to the latest CBSE syllabus of 2022-23.
Exercise 13.1 Introduction Questions & Solutions refer to the below link
Exercise 13.1 Solutions – 3 Questions and Solutions
Exercise 13.2 Conditional Probability – Questions & Solutions refer to the below link
Exercise 13.2 Solutions – 18 Questions and Solutions
Exercise 13.3 Multiplication Theorem on Probability – Questions & Solutions click below.
Exercise 13.3 Solutions – 14 Questions and Solutions
Exercise 13.4 Independent Events – Questions & Solutions click here to know more.
Exercise 13.4 Solutions – 17 Questions and Solutions
Exercise 13.5 Bayes’ Theorem – Questions & Solutions refer to the link below for further details.
Exercise 13.5 Solutions – 15 Questions and Solutions
Exercise 13.6 Random Variables and its Probability Distributions – Questions & Solutions follow the links.
Exercise 13.7 Bernoulli Trials and Binomial Distribution – Questions & Solutions Click on this link
Along with Class 12 Mathematics solutions, you can explore NCERT Solutions on our Extramarks website for all primary and secondary classes.
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NCERT Exemplar for Class 12 Mathematics
NCERT Exemplars are practice books that include additional higher-level questions and are meant to aid meticulous learning. They are mainly used for competitive exams. These topics are up to date, consisting of different topics explained in every chapter of the Class 12 Mathematics book. Students can click on the links for these Exemplar questions and answers for Class 12 Mathematics chapters from the Extramarks website.
Considering the standard and variety, practising Exemplar problems is essential for school boards and competitive examinations. Students can perfectly evaluate themselves by working on these problems and improving their problem-solving skills for future studies. NCERT Solutions Class 12 Mathematics Chapter 13 provides a series of Exemplar Solutions for Class 12 for detailed clarification on all the questions given in the NCERT Exemplar Class 12 books.
Key Features of NCERT Solutions for Class 12 Mathematics Chapter 13
To score well in competitive exams, one should have a solid base in Mathematics. The NCERT books present you with demanding questions that better your analytical skills and give you sufficient exposure to all kinds of questions in any of these exams. Our application is highly beneficial for your preparation for the following reasons.
- NCERT Solutions Class 12 Mathematics Chapter 13 answers to all numerical problems given in the textbook and are given with a step-by-step simplification.
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- Highly detailed answers to all the theoretical as well as logical reasoning questions from the NCERT Solutions Class 12 Mathematics Chapter 13 that are verified by Extramarks subject experts.
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