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# NCERT Solutions for Class 12 Maths Chapter 13 Probability - PDF Download `

NCERT solutions for class 12 maths chapter 13 Probability plays an important role in the development of students’ mathematical skills. The chapter introduces the basic idea of probability. Chapter 13 Probability provides all the essential concepts of conditional probability which help you to understand the Bayes’ theorem, multiplicative probability, and independent of events. This chapter provides an in-depth introduction to Probability. One of the most effective approaches to mastering probability is to study the fundamentals of probability, which is the process of estimating the likelihood of events that are contingent upon the presence of another event. Having an in-depth knowledge of this topic is essential for students to learn how to apply it in practice. Students will be able to solve all the questions in this chapter using NCERT solutions. This will enable them to gain a better comprehension of the method of problem solving.

NCERT solutions for chapter 13 provided by our experienced teachers at eSral are a great help for students to understand probability concepts and perform well in their exams. All the exercise questions in the book are covered by these solutions. Students can also use these NCERT solutions for class 12 mathematics chapter 13 online and download free PDFs for offline practice.

## NCERT Solutions for Class 12 Maths Chapter 13 - Probability I Free PDF

Once you understand the basics of chapter 13 Probability, you'll be able to work with random variables and their probability distribution without any stress. You can find all the formulas and details related to this topic in the pdf form on eSaral website.

### Important Topics Covered in Chapter 13 - Probability

The following is a list of the topics that are included in Chapter 13 of the NCERT solutions class 12 maths.

13.1 Introduction -  This chapter will cover conditional probability, it defines any event that will occur if the other event has already happened. This helps in understanding Bayes' theorem, independent of events and the multiplicative rule in probability. In this chapter, we’ll also look at the probability distribution of the random variables, as well as the mean and variance of the probability distribution. The binomial distribution is sometimes referred to as the discrete probability distribution.

13.2 Conditional Probability

1. Properties of conditional probability

In this section,  you'll find out how if you have two events coming from the same space, how does one of them affect the other? Event B is the conditional probability that it will happen since you already know Event A has happened. P = B|A is the probability that B is going to be the same as A.

13.3 Multiplication theorem on probability - In this section, we'll look at the multiplication theorem on probability.

13.4 Independent Events - Independent events are those events that  when they happen, they don't affect any other events. It's like if you flip a coin and it's going to land on one side. But if you flip it again and it lands on the other, it's going to be the other way around. In other words, independent events are events that happen independently of each other. The set of outcomes is called events, and this is described in detail in the PDF Probability Class 12. If the probability of an event, say A, is independent of the probability of another event, say B, then it is called an independent event.

13.5 Bayes’ Theorem

1. Partition of a sample space

2. Theorem of total probability

Here, you will learn about Bayes' theorem. Bayes' theorem describes the probability of occurrence of an event that is associated with a certain condition. This applies to conditional probability as well.  You will also learn about partition of a sample space and theorem of total probability.

## NCERT Solutions for Class 12 Maths Chapter 13 Exercises

The exercises in chapter 13 have been carefully crafted to improve the students' probability knowledge and problem solving abilities. By solving these exercises, students will have a better understanding of topics and will be better prepared to answer probability questions in exams.

Chapter 13 of class 12 mathematics consists of only four exercises including miscellaneous exercise.

 Exercise 13.1 17 Questions & Solutions Exercise 13.2 18 Questions & Solutions Exercise 13.3 14 Questions & Solutions Miscellaneous Exercise 13 Questions & Solutions

The NCERT solutions for chapter 13 cover every aspect of Probability in an easy-to-understand way. These solutions are explained from the fundamentals of Probability to complex theorems. Here, we will look at the various benefits of using these solutions to improve learning and performance.

1. The solutions are presented in straightforward language, so students don't have to struggle to understand complex topics.

2. NCERT solutions Assist students in reinforcing their fundamental understanding of probability.

3. These NCERT solutions for class 12 mathematics chapter 13 PDF have been prepared using various approaches to provide new solutions to the problems.

4. NCERT solutions for class 12 maths chapter 13 Probability have been prepared and explained by experts, which will help you get good marks.

Question 1. What are the key topics to keep in mind when it comes to chapter Probability?

Answer 1. The NCERT solutions for class 12 maths chapter 13 covers the following important topics:

1. Conditional Probability

A. Properties of conditional probability

2.  Multiplication theorem on probability

3.  Independent Events

4.   Bayes’ Theorem

A. Partition of a sample space

B. Theorem of total probability

Question 2. Why should I practice NCERT solutions for chapter 13 Probability in class 12 maths?

Answer 2. NCERT solutions for chapter 13 Probability are designed to give you an in-depth understanding of how probability works in practice. The practice of the questions included in these solutions is based on probability, which gives clear understanding of concepts. Solving examples and exercises will assist students in developing problem-solving abilities.