The NCERT solutions for the questions given in Chapter 13, Probability, of the Class 12 NCERT textbooks are available here. Probability is the chance of occurrence of an event. In this chapter students learn about Probability in detail. Solving all the questions from this chapter of the NCERT book of class 12 maths, repeatedly, will help the students in understanding the problem solving method.

The class 12 NCERT solutions of the chapter Probability are very easy to understand as the subject experts at BYJU’S ensure that the solutions are given in simplest form. These solutions cover all the exercise questions included in the book and are in accordance with the latest CBSE guidelines. Students can also avail these NCERT solutions and download it for free to practice them offline as well.

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## 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 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

Exercise 13.1 Solutions 17 Questions

Exercise 13.2 Solutions 18 Questions

Exercise 13.3 Solutions 14 Questions

Exercise 13.4 Solutions 17 Questions

Exercise 13.5 Solutions 15 Questions

Miscellaneous Exercise On Chapter 13 Solutions 10 Questions

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

The chapter Probability itself makes up to 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) ≠ 0
P (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) ≠ 0

P (F|E) = P (F), P(E) ≠ 0

- 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 the Chapter 13, Probability, of the NCERT textbook for maths to know more about topics related to Probability.

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

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