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# NCERT Solutions for Class 12 Maths Chapter 13 – Probability

NCERT Solutions for Class 12 Maths Chapter 13- Probability has been prepared to facilitate easy exam preparation and doubt clearance. The chapter consists of various significant concepts such as the light distribution of a random variable, Bayes theorem, multiplication rule of probability, and total probability theorem. It comprises 5 exercises and 1 miscellaneous exercise. They give you ample amounts of practice to become thorough with the various concepts of the chapter. Our NCERT Solutions contain smart, precise, accurate and step by step solutions to all questions of all the exercises.

Our CBSE NCERT Class 12 Maths Chapter 13 solutions have been drafted using the best methods of solving problem sums. They are well-structured and follow a logical flow to help you learn even the most complex topics easily. They have been specifically designed to make learning a very stimulating and highly fruitful process. They are in accordance with the latest CBSE and NCERT guidelines. They not only help you score high marks in your board exams, but they also help you do well in various competitive exams.

## Important topics of NCERT CBSE class 12 Maths Chapters 13

NCERT Solutions for Class 12 Maths Chapter 13- Probability is a continuation of the probability chapter that you learned in class 11. It advanced theorems and complex concepts. Some of them have been discussed below.

Bays Theorem

Under this section of CBSE NCERT Class 12 Maths Chapter 13, you will learn that Bays Theorem is the probability of the occurrence of an event in relation to any condition. The events are also considered as conditional probability. In this section, you will study the Bays theorem formula and proof of Bays theorem.

If A and B are two events, then the formula for Bayes theorem is given by:

P(A|B) = N(A∩B)/N(B); N(B)≠0

Probability distribution

Under this section, you will get to know about the possibilities of each outcome from a random event or experiment. Here you will study the definition of a probability distribution, probability distribution of random variables, categorization of a probability distribution, cumulative, continuous probability distribution, normal probability distribution, binomial probability distribution, negative binomial distribution, Poisson probability distribution, discrete probability, prior probability, and posterior probability.

Total probability theorem

This section helps in building the foundation for understanding advanced concepts of probability. Here you will learn the law of total probability, the total probability statement and the total probability theorem proof.

The formula of total probability theorem is

P(A)=∑k=0nP(Ck)P(A|Ck)

Multiplication rule of probability

Under this section, you will get to know about the multiplication rule of probability. Here you will learn that the multiplication rule of probability explains the condition between two events. For two events A and B related to sample space S, the set A∩B represents the events in which both events A and event B have taken place. Thus, (A∩B) represents the simultaneous occurrence of the events A and B. The event A∩B can be written as AB. The probability of event AB can be calculated by making use of the properties of conditional probability.

The multiplication rule of probability has been represented below.

P(A∩B) = P(A) × P(B|A)

### NCERT Class 12 Maths Chapter 13 Probability Exercises

This chapter comprises 5 comprehensive exercises. Our NCERT Solutions for Class 12 Maths Chapter 13- Probability consist of step by step solutions of all questions of all the exercises of the chapter. The exercises of the chapter have been discussed below.

Exercise 13.1

This exercise will help you in understanding the fundamental concepts of advanced probability. It consists of 17 questions in total. The first ten questions of this exercise are short answer type, and the remaining problems are long answer type. All the questions are related to the conditional probability that follows the pattern of board examination questions.

Exercise 13.2

This exercise of CBSE NCERT Class, 12 Maths Book, consists of a total of 18 questions, all of which long answer type questions. You will have to find out the probability of events from a given condition using multiplication of probability. You will come across questions that comprise of multiple sub-parts.

Exercise 13.3

This exercise of NCERT CBSE Class 12 Maths Chapter 13 helps you to learn methods of solving numerical using Bays theorem. There are 14 questions in this exercise which are long answer type. You will have to calculate the probability of given events and conditions using Bays theorem. Solving this exercise will help you to get develop a clear understanding of working with events like drawing of coloured balls from a bag/box, pack of 52 cards, rolling of a dice, tossing of a fair, and an unbiased coin, etc.

Exercise 13.4

This exercise consists of 17 questions. It shows the methods of solving problems using the distribution of the random variable. The first five NCERT questions of this exercise short answer type questions. Questions 6-15 all long answer type questions that will help you to learn the complicated methods of solving numerical problems related to the distribution of random variables. Question 16 and 17 MCQ type, but you will have to solve numerically to pick the correct alternative.

Exercise 13.5

In this exercise, you will have 15 questions in total, and all are long answer type. These questions help you to become through with the different methods of calculating the probability of a given experiment or event.  It covers various topics of the chapter.

The miscellaneous exercise comprises a total of 17 questions, both long and short answer types that are related to all the topics covered under this chapter.

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

There are a plethora of advantages associated with learning from our comprehensive yet precise solutions.

• The systematic and compact structure of the NCERT Solutions for Class 12 Maths Chapter 13- Probability will help you understand the concepts easily.
• Our NCERT Solutions cover various types of questions according to the question pattern of CBSE.
• Our smart study techniques and learning shortcuts help you learn quickly and score more marks.
• Our NCERT Solutions have been designed to clear all your doubt and improve your retention rate.
• They have been solved using the best methods of solving the problems.
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