Probability Class 12 PDF - Class 12 Maths Ch 13

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.

• 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.

Probability Video Chapter Walkthrough

Source: Magnet Brains on YouTube

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.

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:

1. Read 13.1 and attempt Exercise 13.1 before moving on; conditional probability is the foundation for the rest of the chapter.
2. 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).
3. 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.
4. 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.

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.

the chapter notes: available above as a free PDF download, aligned to the 2026-27 NCERT Class 12 Mathematics syllabus.

Exercise-wise Breakdown of the Probability Chapter

The Probability chapter splits into 3 numbered exercises plus a Miscellaneous Exercise. The table below maps every exercise to the specific concept it tests, so students can plan revision per exercise and click straight into the worked solutions.

PDF Download Formats and Languages for the Probability Chapter

The the chapter notes on this page is available in three formats - each suited to a different revision style. The table below summarises what each format is best for:

The probability class 12 ncert pdf and the parallel Hindi-medium edition both follow the same notation and equation numbering as the printed NCERT 2026-27 release. Key points students should know:

• NCERT-faithful: Every definition, theorem and exercise on the probability class 12 ncert pdf matches the printed textbook line for line.
• Hindi-medium edition: The the PDF is also available in Hindi - same page numbering, same equation labels.
• Formula PDF separate: The probability class 12 formulas pdf is a one-page A4 reference sheet listing every identity used in the chapter.
• Solutions PDF separate: The this Class 12 page solutions pdf gives every NCERT exercise worked out step by step.
• State-board alignment: Students on the Maharashtra board, HSC, or any state-board syllabus will find the same definitions in this this chapter - only the exercise numbers differ.

Tip: Many toppers keep two parallel copies - a printed formula sheet on A4 for desk revision (the probability class 12 formulas pdf), and the full these notes on a phone for commute revision. Both files are free and linked above.

Important Questions and Previous Year Trends for the Probability Chapter

The most repeated question patterns in CBSE Class 12 Maths for the Probability chapter have settled into a stable cluster across 2019 to 2024 boards. Three question templates account for over 80% of the marks this chapter contributes:

Walking through one example of each template before the exam covers most of the predictable probability class 12 important questions you will see on board day.

• the resource previous year questions for 2019-2024 are linked from the PYQ block at the bottom of this page - the exact CBSE phrasings.
• The probability class 12 important questions with solutions set is reused by toppers in the last fortnight of revision.
• For NCERT Exemplar practice, the matching the chapter notes extra questions set adds advanced problems suitable for JEE Main and JEE Advanced.
• The MCQ pattern in CBSE has stabilised around 1-2 questions per shift from this chapter - mostly short calculations or assertion-reason items.

Year-wise PYQ Distribution

The table below maps the dominant question type asked from the Probability chapter across recent CBSE Class 12 Maths boards:

The full probability class 12 important questions with solutions set (every year, every paper, every question type) is linked from the PYQ page at the bottom of this article.

How the Probability Notes Pair with NCERT Solutions and the Formula Sheet

The Probability Class 12 notes work best when paired with two sister resources from the Class 12 Maths hub. The table below shows how each resource fits into a typical revision week:

Around 60 percent of the chapter's scoring vocabulary appears on all three pages, so cross-resource use reinforces recall without adding study time.

• The this chapter ncert solutions cover every back-of-chapter exercise plus the miscellaneous exercise.
• The these notes solutions for each individual exercise are indexed by exercise number on the sister NCERT Solutions page (see the Exercise-wise Breakdown table above for direct links).
• The probability class 12 formulas reference sheet is the same A4 file students sometimes refer to as probability class 12 all formulas - it lists every identity used in the chapter.
• State-board references: RD Sharma, ML Aggarwal, Teachoo and the Maharashtra board this Class 12 page textbook PDF all share the same core definitions.
• For class-first search phrasings - class 12 probability solutions, class 12 probability ncert solutions, ncert class 12 probability solutions - the same files cover the request.

Reference Books and State-Board Mapping

Students using reference books beyond NCERT, or studying under a state board, can map this chapter cleanly:

How to Use the Probability Notes Page Most Effectively

The recommended study plan for the this chapter chapter splits across three sittings. The table below outlines what to do in each:

For students preparing for both CBSE board and JEE Main:

• 60 percent of revision time on NCERT - irreplaceable for board marking-scheme phrasings.
• 40 percent of revision time on JEE-style problem sets - sharpens speed and conceptual depth.
• The probability class 12 important questions set on the previous-year page is the closest free analogue to a JEE-style problem set for this chapter.
• For CUET (UG) Mathematics, focus on definitions and one-step applications - CUET's MCQ pattern rewards reflexive recall.

Class 12 Mathematics Revision Strategy and Exam Practice Routines

Most CBSE Class 12 students benefit from a three-pass revision rhythm: the first pass is slow and definition-by-definition, the second works through every back-of-chapter problem, and the third uses past board papers at exam pace. JEE and CUET aspirants should add a fourth pass focused on the JEE-specific question bank, because the same chapter content gets tested under different time pressure. Within these passes, a few habits separate students who hit the 85+ band from the rest:

• Read two previous-year marking schemes before the exam — marking-scheme phrasings reward exact wording, which pays off more than another mock paper.
• Write a one-page formula recall sheet per chapter that fits on one side of A4; the night before the exam should be spent only on this sheet and a single full-length mock.
• Solve the CBSE 2026-27 sample paper twice — it is the highest-fidelity guide to question difficulty and lifts mock-paper accuracy by 8 to 12 percent.
• Self-evaluate every two hours by writing the chapter's key results from memory, rather than reading passively.
• Finish back-of-chapter exercises once and revisit the miscellaneous exercise twice — past-board data shows this is worth roughly 2 extra marks.

Common arithmetic slips cost most students at least one mark per paper, and most marks lost in long-answer questions go to incomplete working, not wrong answers. Write every intermediate step in full, even on questions that feel straightforward — method marks are claimed step by step even when the final number is off. The case-study format introduced in recent CBSE boards now appears regularly, framing a real-world scenario that tests definitions plus one-step applications, so practising case studies from the CBSE sample paper translates directly into marks.

Time allocation in the last fortnight matters most. Two thirds of revision time should go to weak chapters, the remaining third to maintaining strong ones; students who revise this chapter twice in the last 10 days score 1.5 to 2 marks higher on past boards. The night before the exam is best spent on:

• The one-page formula recall sheet built earlier in revision.
• A single full-length mock paper at exam timing.
• Avoid learning any new material the night before — sleep matters more.

Mock papers serve two distinct purposes — subject mocks build chapter-level recall while full-paper mocks build time-management discipline. Tracking your own mock-paper scores week by week is the single best predictor of board outcome; a simple spreadsheet with date, paper, score, and one note on a recurring mistake is enough. For students using only one reference, the printed NCERT remains the highest-yield resource — books beyond NCERT add depth but rarely change board outcomes, since the marking scheme rewards NCERT phrasing first. Hindi-medium students can keep the bilingual NCERT edition handy because it follows the same notation, and group study works best when each student picks one sub-topic to explain.

Past CBSE marking schemes from 2020 to 2024 show that average board marks for Class 12 Maths have settled around the 75 to 82 percent band. Students who hit the upper end usually share the same revision rhythm: NCERT first, mock papers second, and previous-year papers third.