NCERT Solutions for Class 12 Maths Chapter 13.3 Probability

NCERT Solutions for Class 12 Maths Chapter 13.3: Probability is the measurement of likelihood of an event happening in a random experiment. The NCERT Solutions for Probability exercise 13.3 Class 12 Maths deals with concepts of Bayes’ theorem. The questions are based on the first subsection, partition of a sample space, and the second subsection, theorem of total probability. In ex 13.3 Class 12, there are 14 questions to practice. 

Class 12 Maths Chapter 13 talks about Conditional Probability and its Properties, Multiplication Theorem on Probability, Probability Distribution of a Random Variable, Mean and Variance of a Random Variable and many more. Embibe delivers a set of 400+ practice questions for all the sub-topics included in Chapter 13. Students must practice the in-text questions provided by Embibe without fail. Scroll down to access the NCERT Solutions for Class 12 Maths Chapter 13 and important topics.

NCERT Solutions for Class 12 Maths Chapter 13: Important Topics

Probability chapter of Class 12 Maths may seem confusing to many students. However, as students learn the basics of the concept and solve numerous example problems, the get familiar with the questions. Gradually, problem-solving becomes easy and students will find the topic of Probability very interesting to learn. Solving the NCERT solutions for Chapter 13 provided in this chapter is the easiest way to become proficient in the topic and score good marks.

Embibe offers all the solutions of Class 12 Chapter 13 Maths for and they are designed based on the latest syllabus. Also, students can find NCERT 3D Videos, NCERT Exemplars, Embibe Explainers, etc., for on Embibe.

Before moving on to access the solutions of Probability chapter, let us know the important topics of the chapter.

NCERT Solutions for Class 12 Maths Chapter 13: Points to Remember

Below-mentioned are some of the important points related to Class 12 Maths Chapter 13 Probability. Students must make a note of these points so that they can be revised easily during final examinations.

Below we have provided some of the important points to remember for NCERT Class 6 Science Chapter 11 to ace your exams:

• Elementary event: If a random experiment is performed, then each of its outcomes is known as an elementary event.
• Sample space of an experiment: The set of all possible outcomes of a random experiment is called the sample space associated with it and it is generally denoted by S
• Simple event and Compound event: A subset of the sample space associated to a random experiment is said to define a simple event if it has only one outcome.
  A subset of the sample space associated to a random experiment is said to define a compound event if it has more than one outcome.
• Favourable elementary events: Let S be the sample space associated with a random experiment and A be an event associated to the experiment. Then elementary events belonging to A are known as favourable elementary events to the event A.
• Probability of an event: If there are n elementary events associated with a random experiment and m of them are favourable to an event A, then the probability of happening or occurrence of A is denoted by P(A) and is defined as the ratio m/n.
• Let S be the sample space associated with a given random experiment. Then, a real valued function X which assigns each event w ∈ S to a unique real number X (w) is called a random variable.
• The conditional probability of an event E, given the occurrence of the event F is given by P(E/F)= P(E ∩ F)/P(F), P(F) ≠ 0
• 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 Let {E1 , E2 , …,En ) be a partition of a sample space and suppose that each of E1 , E2 , …, En has nonzero probability. Let A be any event associated with S, then, 
• P(A) = P(E1 ) P (A|E1 ) + P (E2 ) P (A|E2 ) + … + P (En ) P(A|En ) 
• Bayes’ theorem If E1 , E2 , …, En are events which constitute a partition of sample space S, i.e. E1 , E2 , …, En are pairwise disjoint and E1 E2 … En = S and A be any event with nonzero probability, then,
• P(E A P(E ) P (A|E ) P(E )P (A|E )
• A random variable is a real valued function whose domain is the sample space of a random experiment.
• Var (X) = E (X2 ) – [E(X)]2
• Trials of a random experiment are called Bernoulli trials provided they satisfy the following conditions : (i) There must be a finite number of trials. (ii) The trials must be independent. (iii) Each trial must have exactly two outcomes i.e. success or failure. (iv) The probability of success remains the same in each trial

NCERT Solutions for Class 12 Maths: All Chapters

Students can access the NCERT solutions for all chapters of Class 12 Maths from below.

• Chapter 1: Relations and Functions
• Chapter 2: Inverse Trigonometric Functions
• Chapter 3: Matrices
• Chapter 4: Determinants
• Chapter 5: Continuity and Differentiability
• Chapter 6: Applications of Derivatives
• Chapter 7: Integrals
• Chapter 8: Application of Integrals
• Chapter 9: Differential Equations
• Chapter 10: Vector Algebra
• Chapter 11: Three Dimensional Geometry
• Chapter 12: Linear Programming

FAQs on NCERT Solutions for Class 12 Maths Chapter 13.3

Q.1. Where can I download Class 12 Maths Chapter 13 Probability NCERT Solutions?
Ans. Students can download the NCERT Solutions for Class 12 Maths Chapter 13 from this page of Embibe. It can also be downloaded from the NCERT official website.

Q.2. Is studying from NCERT Solutions Class 12 Maths sufficient to pass the board exam?
Ans. Yes, the NCERT textbooks and NCERT Solutions are the prescribed books for Class 12. These books are typically enough for the Class 12 board exam. Students who want to refer to advanced books are advised to strengthen their basics from the NCERT books and then study from reference books.

Q.3. Can I study the Class 12 Maths NCERT Solutions Chapter 13 without solving 13.3 and other exercises?
Ans. No, students need to practise the questions given in Chapter 13, examples of probability, to solve questions accurately in the final exam. 

Q.4. Can I download the conditional probability examples and solutions for Class 12 Maths NCERT Solutions from Embibe?
Ans. Students can download the NCERT Solutions Class 12 Maths solved examples of probability from this article.

Q.5. How many exercises are there in NCERT Solutions for Class 12 Maths Chapter 13?
Ans: There are five exercises with conditional probability examples and solutions in the NCERT Solutions for Probability Class 12 Maths Chapter 13. There are also two miscellaneous questions based on the whole chapter that students can practice.