## Probability NCERT Solutions Class 12 Maths Chapter 13 Exercise 13.1 13.2 13.3 13.4 13.5 Miscellaneous Free pdf Notes Study Material download-Anand Classes |

**NCERT Solutions for Class 12 Maths Chapter 13 Probability** has been published by ANAND CLASSES. Students can now download the **Class 12 Maths Ch 13 Questions and Answers PDF** here. These NCERT Solutions for Class 12 Maths contains answers of all questions asked in Chapter 13 in textbook. Therefore you can refer it to solve Probability exercise questions and learn more about the topic.

# Download the pdf of NCERT Solutions for Class 12 Maths Chapter 13 – Probability

## NCERT Solutions for Class 12 Maths Chapter 13 – Probability

The major concepts of Maths covered in Chapter 13 – Probability of **NCERT Solutions** for Class 12 includes

**13.1 Introduction****13.2 Conditional Probability****13.2.1 Properties of Conditional Probability****13.3 Multiplication Theorem on Probability****13.4 Independent Events****13.5 Bayes’ Theorem****13.5.1 Partition of a Sample Space****13.5.2 Theorem of Total Probability****13.6 Random Variables and Their Probability Distributions****13.6.1 Probability Distribution of a Random Variable****13.6.2 Mean of a Random Variable****13.6.3 Variance of a Random Variable****13.7 Bernoulli Trials and Binomial Distribution****13.7.1 Bernoulli Trials****13.7.2 Binomial Distribution**

The chapter, Probability itself, makes up a whole unit, Unit Six – Probability, that carries 8 marks of the total 80 marks. There are 2 exercises, along with a miscellaneous exercise in this chapter, to help students understand the concepts related to Probability thoroughly. Some of the topics discussed in Chapter 13 of **NCERT Solutions for Class 12** Maths are as follows:

- 0 ≤ P (E|F) ≤ 1, P (E′|F) = 1 – P (E|F)P ((E ∪ F)|G) = P (E|G) + P (F|G) – P ((E ∩ F)|G)
- P (E ∩ F) = P (E) P (F|E), P (E) ≠ 0P (E ∩ F) = P (F) P (E|F), P (F) ≠ 0
- If E and F are independent, then P (E ∩ F) = P (E) P (F)P (E|F) = P (E), P (F) ≠ 0P (F|E) = P (F), P(E) ≠ 0
- The theorem of total probability
- Bayes’ theorem
- A random variable is a real-valued function whose domain is the sample space of a random experiment.
- Var (X) = E (X
^{2}) – [E(X)]^{2} - Trials of a random experiment are called Bernoulli trials if they satisfy the following conditions :
- There should be a finite number of trials.
- The trials should be independent.
- Each trial has exactly two outcomes: success or failure.
- The probability of success remains the same in each trial.

Go through Chapter 13 Probability of the NCERT textbook for Maths to know more about topics related to Probability. Students can utilise the **NCERT Solutions for Class 12 Maths Chapter 13** for any quick reference to comprehend complex topics.

## Features of NCERT Solutions for Class 12 Maths Chapter 13 – Probability

Studying the chapter “Probability” of Class 12 NCERT Solutions enables the students to understand Conditional probability, multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, and mean and variance of a random variable.

## Frequently Asked Questions (FAQs) on NCERT Solutions for Class 12 Maths Chapter 13

**Q1**

### List out the topics and sub-topics covered in Chapter 13 of NCERT Solutions for Class 12 Maths.

- The topics and subtopics covered in Chapter 13 of NCERT Solutions for Class 12 Maths are listed below.

13.1 Introduction

13.2 Conditional Probability

13.2.1 Properties of Conditional Probability

13.3 Multiplication Theorem on Probability

13.4 Independent Events

13.5 Bayes’ Theorem

13.5.1 Partition of a Sample Space

13.5.2 Theorem of Total Probability

13.6 Random Variables and its Probability Distributions

13.6.1 Probability Distribution of a Random Variable

13.6.2 Mean of a Random Variable

13.6.3 Variance of a Random Variable

13.7 Bernoulli Trials and Binomial Distribution

13.7.1 Bernoulli Trials

13.7.2 Binomial Distribution

**Q2**

### Explain the concept of conditional probability in Chapter 13 of NCERT Solutions for Class 12 Maths.

**Q3**

### Why NCERT Solutions for Class 12 Maths Chapter 13 is beneficial for the students to score well in the board exams?

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