# NCERT Solutions for Class 12 Maths Chapter 13 Probability

NCERT Solutions for Class 12 Maths Chapter 13: Probability refers to the likelihood of an event occurring. You can learn about probability in-depth in this chapter. You will gain a better knowledge of the problem-solving approach in Chapter 13 if you solve all of the questions from Probability Class 12 NCERT Solutions.

The Class 12 NCERT Solutions for the chapter Probability are very simple to grasp since KopyKitab’s experts make sure that the solutions are presented in the simplest form possible. Go through the blog to download the exercise-wise Probability Class 12 NCERT Solutions PDFs!

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

NCERT Solutions for the questions in Chapter 13 Probability of the Class 12 NCERT textbooks are provided below:

Class-12-Mathematics-Solutions-Chapter-13 pdf

## What will you get in Probability Class 12 NCERT Solutions for Class 12 Maths?

Go through the subtopics discussed in NCERT Solutions for Class 12 Maths Chapter 13:

 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

### NCERT Solutions for Class 12 Maths Chapter 13 exercises-

 Exercise Solutions 13.1 17 Questions Exercise Solutions 13.2 18 Questions Exercise Solutions 13.3 14 Questions Exercise Solutions 13.4 17 Questions Exercise Solutions 13.5 15 Questions Misc.Exercise Solutions 13.6 10 Questions

### CBSE Chapter 13 Class 12 Maths- Probability: 13.1: Introduction

This section will teach you about the concepts about conditional probability, which will eventually help you work on Bayes’ theorem, independence of events along multiplication rule in probability. Well, there is more to study from this chapter, for now; let’s proceed with the next section which is a conditional probability.

### CBSE Chapter 13 Class 12 Maths- Probability: 13.2: Conditional Probability

This section is simple and teaches you about how one single event might be responsible for changing the events of another corresponding event. The chapter covers all the minute details depicting the situation with quality examples which will be sufficient to get a thorough idea to work with the sums.

### CBSE Chapter 13 Class 12 Maths- Probability: 13.3: Multiplication Theorem on probability

Once you learned and understood the conditional probability, getting to know and study this notion becomes a lot easier. Probability NCERT Solutions Class 12 is a substantial study resource. Therefore with this course content students are bound to grasp the topic in no time. Additionally, since the chapter is practical in tone, make sure to maintain a regular practice session.

### CBSE Probability NCERT Solutions Class 12: 13.4:  Independent Events

This section talks about those events which occur without affecting any other of that sort. Take, for instance, you flip a coin, you already assume that there is a general outcome of the event. Either it’s a tail or a head, isn’t it? And in each situation, none of the events affects the other.

With a thorough study session on the NCERT Solutions for Class 12 Maths Chapter 13 and several practice sessions we assure you, you will get every corner of the section competently.

### CBSE Probability NCERT Solutions Class 12: 13.5:  Bayes’ theorem

This section introduces you to Bayes’ theorem which teaches about the probability of an event occurring which is relevant to any conditions. Well, this situation often resembles conditional probability.

Take, for instance, you own a bag that has three balls of three different colors, which are blue, yellow, and red. You will have to estimate the probability of taking out the number of yellow balls from the three colors. In this situation, the event occurring is measured depending on the other probable conditions which is the conditional probability.

### CBSE Probability NCERT Solutions Class 12: 13.6 Random Variables and its Probability distribution

The probability of distribution of a random value is what determines the probability of its value which is unknown. A random variable can either be continuous or discrete or both. The chapter is loaded with many interesting notions for you to discover once you grab your NCERT Solutions for Class 12 Maths Chapter 13 from here.

### CBSE Probability NCERT Solutions Class 12: 13.7: Bernoulli Trial and Binomial Distribution

Here in this portion of the chapter, you will get a close look at the Bernoulli trial and Binomial distribution but in brief. Bernoulli trial or binomial trial comes out with only two possible results. Get yourself CBSE class 12 maths – chapter 13 pdf to jet start your exams preparation right here, right now.

## CBSE Class 12 Maths- Chapter 13: Important theories and formulas

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, thenP (E ∩ F) = P (E) P (F)P (E|F) = P (E), P (F) ≠ 0P (F|E) = P (F), P(E) ≠ 0
4. 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
9. 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.

## Benefits of NCERT Solutions for Class 12 Maths Chapter 13

#### Go through few benefits of using NCERT Solutions for Class 12 Maths Chapter 13:

1. Assist students with their homework and competitive tests.
2. Content is well-structured.
3. Assist students in reinforcing their fundamental understanding of probability.
4. Subject expertise assisted in the preparation of these NCERT Solutions.

Well, we have jotted down every possible point for CBSE from NCERT Solutions for Class 12 Maths Chapter 13. Still, if you have any queries, feel free to ask in the comment section below.

### What is conditional probability?

Conditional probability describes the likelihood of events that occur in relation to one or more other events.

### How many questions were there in exercise 13.5 of chapter 13 Maths class 12?

There are a total of 15 questions in exercise 13.5 of chapter 13 Maths class 12.

### Can I get an overview of the Ch 13 Maths Class 12 Solutions exercises?

Yes. You can receive an overview of the Ch 13 Maths Class 12 Solutions exercises from the above blog.

### How many exercises are there in NCERT Solutions for Class 12 Maths Chapter 13?

In total, there are 5 exercises in Chapter 10 Class 12 Maths.

### Where can I download Maths Chapter 13 Class 12 NCERT solutions?

You can download NCERT Solutions for Class 12 Maths Chapter 13 from the above blog.

### Is NCERT Solution for Class 12th Maths sufficient for Chapter 13 preparation?

Yes. NCERT Solution for Class 12th Maths is sufficient for Chapter 13 preparation.