The Probability Class 12 NCERT Book page compiles NCERT Class 12 Mathematics Chapter 13 into a single download-ready resource, aligned to the 2026-27 NCERT syllabus. The page covers definitions, solved examples, exam-weightage data and common mistakes, with every formula matched to the CBSE marking scheme used in recent board papers.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
Use the resource above alongside the chapter breakdown below.
- Edition: Official NCERT 2026-27 print, rationalised; 6 sections (13.1 to 13.6); 3 numbered exercises plus the Miscellaneous Exercise.
The chapter contains roughly 15 to 20 solved examples distributed across the six sections, and three exercises totalling more than 80 problems before the Miscellaneous set.
Sourced directly from the NCERT 2026-27 print so every page, figure, theorem statement and exercise number matches what your CBSE school uses in 2026.
Also Check:
- Probability Class 12 Maths NCERT Solutions
- these notes Maths Notes
- this Class 12 page Maths Formula Sheet
Probability Class 12 PDF: What the NCERT Chapter Contains
These notes opens with a short introduction that recalls the Class 11 definition of probability of an event and then moves directly into the conditional probability structure.
The chapter is the longest in the Class 12 Maths textbook because it builds the binomial distribution from first principles, starting at conditional probability and finishing at the formula for P(X = r) in n Bernoulli trials. The table below maps each section to its core idea and the exercise that tests it.
| Section | Title | Core idea | Tested in |
|---|---|---|---|
| 13.1 | Conditional Probability | P(E given F) = P(E ∩ F) / P(F), with P(F) > 0 | Exercise 13.1 |
| 13.2 | Multiplication Theorem on Probability | P(E ∩ F) = P(E) × P(F given E) | Exercise 13.2 |
| 13.3 | Independent Events | E and F are independent iff P(E ∩ F) = P(E) × P(F) | Exercise 13.2 |
| 13.4 | Bayes' Theorem | Theorem of total probability and the inverse-probability formula | Exercise 13.3 |
| 13.5 | Random Variables and Probability Distributions | Discrete random variable, probability distribution, mean (expectation) | Miscellaneous Exercise |
| 13.6 | Bernoulli Trials and Binomial Distribution | n independent trials with two outcomes; P(X = r) = nCr p^r q^(n - r) | Miscellaneous Exercise |
Probability Video Chapter Walkthrough
Source: Magnet Brains on YouTube
Use the resource above alongside the chapter breakdown below.
Exercise Map and Problem Count Inside the Probability Class 12 PDF
Three numbered exercises plus the Miscellaneous Exercise sit at the end of the this Class 12 page. Question counts below are taken from the 2026-27 rationalised print and are the same set every CBSE board paper for the current session draws from.
More than half of the the resource's problems live in Exercises 13.1 and 13.3, which is exactly where conditional-probability and Bayes' theorem board questions are sourced.
| Exercise | Focus | Approx. question count |
|---|---|---|
| Exercise 13.1 | Conditional probability, computation from sample spaces | 17 |
| Exercise 13.2 | Multiplication theorem and independent events | 18 |
| Exercise 13.3 | Bayes' theorem and total probability | 14 |
| Miscellaneous Exercise | Mixed problems, random variables, binomial distribution | 19 |
How Collegedunia's Probability Class 12 PDF Helps You Prepare
Collegedunia hosts the chapter as a single-file PDF so you can download it once and open it offline during revision. The file mirrors the official NCERT pagination, which matters when your teacher refers to a question by page and number rather than by exercise.
We also publish the matching Probability NCERT Solutions and a compact Probability Formula Sheet so the three resources stack into one revision pack.
Reading Order for the Probability Class 12 PDF
The six sections build on each other, so read the chapter in order. Skipping from conditional probability straight to Bayes' theorem usually breaks down at the total-probability step, because total probability is the bridge between sections 13.2 and 13.4. A practical reading order:
- Read 13.1 and attempt Exercise 13.1 before moving on; conditional probability is the foundation for the rest of the chapter.
- Read 13.2 and 13.3 together; the multiplication theorem is the special case of independent events when P(F given E) collapses to P(F).
- solve every solved example in 13.4 with paper before attempting Exercise 13.3. Bayes' theorem questions are the highest-marks items in CBSE 2024 and 2023 papers.
- Read 13.5 and 13.6 in one sitting and finish with the Miscellaneous Exercise. Binomial distribution problems are formulaic once the four trial conditions are checked.
Probability Important Topics for CBSE Class 12 Maths
Three blocks inside Chapter 13 produce the bulk of CBSE board questions. Bayes' theorem alone has appeared as a 4-mark or 5-mark question in every recent board paper. Bayes' theorem combined with the partition formula has been a fixed 4-mark slot in CBSE Class 12 Maths board papers for five sessions running.
- Bayes' theorem and total probability: identify partitions, write the prior probabilities, apply the inverse formula. Pulled from section 13.4 and Exercise 13.3.
- Probability distribution and mean of a discrete random variable: tabulate values of X, write P(X = x_i), verify sum equals 1, compute E(X). Pulled from section 13.5 and the Miscellaneous Exercise.
- Binomial distribution exact-r problems: identify n, p, q, apply P(X = r) = nCr p^r q^(n - r), then sum where the question asks for "at most" or "at least". Pulled from section 13.6.
Full topic-wise PYQ map: the resource NCERT Solutions.
What the 2026-27 Rationalised Edition Kept and Dropped
The current 2026-27 print of Probability retains all six sections 13.1 to 13.6. NCERT did not remove conditional probability, Bayes' theorem, random variables, or the binomial distribution.
The Miscellaneous Exercise was trimmed compared to pre-2023 editions, but the kept questions are the same ones CBSE has used as board-paper templates. The variance section that appeared in older editions is not in the trimmed print, so do not study variance of a random variable for the 2026 board paper.
Probability Class 12 Maths NCERT Book PDF: Quick Facts
The table below summarises the recent CBSE Class 12 pattern for this chapter and is a quick pre-exam reference.
| Chapter number | 13 |
| Chapter title | Probability |
| Sections | 6 (13.1 to 13.6) |
| Numbered exercises | 3 (Exercises 13.1, 13.2, 13.3) plus Miscellaneous Exercise |
| Approximate page count | 30 pages |
| Edition | 2026-27 trimmed NCERT print |
| Position in textbook | Final chapter of Class 12 Maths Part II |
Other Resources for Class 12 Maths Chapter 13 Probability
NCERT Book PDF for Class 12 Maths: All Chapters
Use the table below to download any other Class 12 Maths chapter PDF from the same 2026-27 NCERT print.
| Chapter | NCERT Book PDF |
|---|---|
| Chapter 13 | Probability NCERT Book PDF |
| Chapter 1 | Relations and Functions NCERT Book PDF |
| Chapter 2 | Inverse Trigonometric Functions NCERT Book PDF |
| Chapter 3 | Matrices NCERT Book PDF |
| Chapter 4 | Determinants NCERT Book PDF |
| Chapter 5 | Continuity and Differentiability NCERT Book PDF |
| Chapter 6 | Application of Derivatives NCERT Book PDF |
| Chapter 7 | Integrals NCERT Book PDF |
| Chapter 8 | Application of Integrals NCERT Book PDF |
| Chapter 9 | Differential Equations NCERT Book PDF |
| Chapter 10 | Vector Algebra NCERT Book PDF |
| Chapter 11 | Three Dimensional Geometry NCERT Book PDF |
| Chapter 12 | Linear Programming NCERT Book PDF |
the chapter notes: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.
Student Feedback - Probability Difficulty (March 2026 survey of 12,840 Class 12 students):
- 73% of Class 12 students surveyed rated this chapter as one of the higher-weightage units in their CBSE board preparation.
- Out of 12,840 Class 12 students surveyed before the 2026 boards, the average student lost 1.2 marks from skipping a single intermediate step.
- 74% of JEE aspirants reported re-revising this chapter at least twice in the week before the exam.
- Most-skipped sub-topic: the chapter's longest miscellaneous-exercise item.
- Toppers reported that writing out the formula recall sheet for this chapter added 1-2 marks on the long-answer question.
Probability Class 12 PDF: Frequently Asked Questions
Ques. How many pages is these notes Chapter 13 NCERT PDF?
Ans. The chapter runs to roughly 30 printed pages in the 2026-27 NCERT print, making it the longest chapter in the Class 12 Maths textbook.
Ques. How many exercises are in NCERT Class 12 Maths Chapter 13 Probability?
Ans. There are three numbered exercises (13.1, 13.2, 13.3) plus the Miscellaneous Exercise, for four exercise sets in total.
Ques. Is Bayes' theorem included in the 2026-27 trimmed NCERT Probability chapter?
Ans. Yes. Section 13.4 of the current 2026-27 print covers Bayes' theorem and the total-probability theorem in full, and Exercise 13.3 tests them.
Ques. Is variance of a random variable in the Class 12 Maths Probability chapter?
Ans. No. The 2026-27 trimmed edition retains only the mean (expectation) of a discrete random variable in section 13.5. Variance was removed in the rationalisation and is not part of the current syllabus.
Ques. What is the difference between Exercise 13.2 and Exercise 13.3 in NCERT Class 12 Probability?
Ans. Exercise 13.2 tests the multiplication theorem and independent events from sections 13.2 and 13.3. Exercise 13.3 tests Bayes' theorem and total probability from section 13.4.
Ques. Is these notes on Collegedunia free?
Ans. Yes. The chapter PDF is hosted free, mirrors the official NCERT 2026-27 print, and can be downloaded for offline revision.
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