## Revision Notes for CBSE Class 12 Maths Chapter 12 (Linear Programming) - Free PDF Download

## FAQs on Probability Class 12 Notes CBSE Maths Chapter 13 [Free PDF Download]

1. What is the Multiplication Rule of Probability? What is the Multiplication Rule for Three Events?

Let suppose that A and B are two events associated with a sample space A, then the probability of occurrence simultaneously of the events A and B is:

P(A ∩ B) = P(A) × P(B/A), where P(F) ≠ 0.

This rule is termed a multiplication rule of probability.

The multiplication rule can be generalized for Three Events: If A, B, and C are three events of sample space, then:

P(A∩B∩C) = P(A) × P(B/A) × P(C/A∩B)

2. State Bayes Theorem.

Let us suppose A_{1}, A_{2}, A_{3}...A_{n} are non-empty events. These events partition the sample space S. That is A_{1}, A_{2}, A_{3}...An are pairwise disjoint and A_{1}ሀA_{2}ሀA_{3}...ሀA_{n} = S. Also, each A_{i} > 0 ∀ i = 1, 2, 3, ...n. Also, let X be a non-zero event then the probability:

P(A_{i}/X) = [P(A_{i}) × P(X/A_{i})]/[Σ_{i=1}^{n} P(A_{i}) P(X/A_{i})]

3. What is Booley’s Inequality?

Let us suppose E_{1}, E_{2}, E_{3},...E_{n} are events associated with a sample space S of an experiment. Then according to Booley’s inequality:

(a) P(E_{1}∩E_{2}∩E_{3}∩...∩E_{n}) ≥ Σ_{i=1}^{n} P(E_{i}) - (n - 1)

(b) P(⋃_{i=1}^{n} E_{i}) ≤ Σ_{i=1}^{n} P(E_{i})

4. Can I download the Notes for Chapter 13 Probability of Class 12 Maths in PDF?

Yes. Students can download the notes of the chapter probability from the official website of Vedantu. Open the Vedantu website, select study material and then CBSE. Under the CBSE, select Revision notes and then Class 12 revision notes. Students will be directed to a new page where they can find all the chapters of Maths for Class 12. Select Chapter 13- Probability. Students now can view the notes offline or download them in PDF format.

5. How many questions are there in Chapter 13 Probability of Class 12 Maths?

There are a total of five exercises containing 81 questions in Class 12 Maths Chapter 13 Probability. All the questions test the students how much they have understood the topics. Students can plan a strategy to make their preparation easier and gain a strong foundation on the topics by analyzing the number of problems given in each section. The format of these solutions is in such a way that students gain a sound knowledge of all the important concepts and basics based on conditional probability.

6. What are the important topics covered in Chapter 13 Probability of Class 12 Maths?

Chapter 13 Probability of Class 12 Maths explains to the students all the significant properties and theorems of conditional probability. The important topics that are covered in this chapter are based on the theorems and terms related to conditional probability such as multiplication theorem on probability, Bayes’ theorem, mean and variance of a random variable, independent events, total probability, random variables, and its probability distribution. Solving all the questions based on these will help the students to improve their fundamental knowledge of probability. The main aim of framing such solutions is to help the students in their studies by promoting math proficiency.

7. What are the importance of NCERT Solutions and revision notes for Chapter 13 Probability of Class 12 Maths?

NCERT Solutions and revision notes for Chapter 13 Probability of Class 12 Maths are very important to study materials as it makes the students gain a clear knowledge of conditional probability. It will help the students to understand the various applications of probability in different fields. The format of these solutions is framed in such a way that it will help to raise the mathematical learning and confidence in students. Practising the questions with these resources makes the students gain a sense of self-accomplishment and confidence which is required to face various competitive exams.

These solutions are available on Vedantu's official website(vedantu.com) and mobile app free of cost.

8. Why should I practice NCERT Solutions for Chapter 13 Probability of Class 12 Maths?

NCERT Solutions for Chapter 13 Probability of Class 12 Maths are well created to make the students obtain a deep understanding of the practical applications of probability. Students should practice the sample problems which are provided in these solutions as they are based on the practical observation of probability in our environment. Students can improve their problem-solving skills by working with examples from their daily lives. It will also help them to improve their mental abilities to work around the most difficult situations.