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# 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:

1. 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)
2. P (E ∩ F) = P (E) P (F|E), P (E) ≠ 0P (E ∩ F) = P (F) P (E|F), P (F) ≠ 0
3. 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
4. The theorem of total probability
5. Bayes’ theorem
6. A random variable is a real-valued function whose domain is the sample space of a random experiment.
7. Var (X) = E (X2) – [E(X)]2
8. Trials of a random experiment are called Bernoulli trials if they satisfy the following conditions :
1. There should be a finite number of trials.
2. The trials should be independent.
3. Each trial has exactly two outcomes: success or failure.
4. 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.

Conditional probability explains the probability of events that takes place in relation to one or more events. Consider A and B are two events that are associated with the same sample space of a random experiment, so the conditional probability of event A will be under the condition of which event B has occurred.
Q3

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

NCERT Solutions for Class 12 Maths Chapter 13 is provided by the experts at ANAND CLASSES’S in accordance with the understanding abilities of students. The solution module PDF can be downloaded from ANAND CLASSES’S based on the requirements of students. All the important concepts from the exam point of view are explained in simple language to help students ace the board exam without fear. The solutions for all the problems present in the NCERT textbook help students cross-check their answers and analyse their areas of weakness.

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