The Probability Class 12 Handwritten Notes 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.
- Style: Scanned notebook PDF (blue + red ballpoint, ruled A4)
- Pages: 19 pages, hand-lettered at written-by-hand pace
- Syllabus: CBSE Class 12 Mathematics 2026-27 (current NCERT print)
The notebook holds 7 Venn diagrams, 5 tree diagrams, 1 binomial table and 11 solved problems across 19 pages.
Student Pulse - 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.
Also Check: The same chapter is also available in typeset Notes and full NCERT Solutions.
Hand-lettered by Class 12 Maths specialists at Collegedunia; mapped 1-to-1 to the official 2026-27 NCERT chapter ordering.
Probability class 12 mathematics handwritten notes: why this format works
Probability is the rare Class 12 chapter where the visual layout of the answer carries half the marks. A Bayes' Theorem question with a clean two-stage tree diagram and labelled branch probabilities is far easier to follow than the same answer written as flat algebra.
Handwritten notes preserve that spatial logic. Roughly 8 marks of the CBSE Class 12 Maths paper come from Probability every year, and the notebook walks through each derivation in the same hand you will use in the exam hall.
The pen-colour convention used throughout the Probability and Statistics Handwritten Notes:
- Blue ink: definitions, body text, working steps
- Red ink: final formulae, boxed results, exam-tag warnings
- Pencil shading: Venn-diagram overlaps and sample-space regions
Probability Video Walkthrough
Source: Magnet Brains on YouTube
What's inside the Probability handwritten notes PDF
The 19 pages of the notebook follow the NCERT 2026-27 section order. The pen-coloured headers on each page act as a built-in table of contents, so you can flip to a topic without a separate index.
| Page | Topic covered | Hand-drawn elements |
|---|---|---|
| 1-2 | Recap of probability axioms, sample space, events | 2 Venn diagrams (union, intersection) |
| 3-5 | Conditional probability P(A|B), solved definition | 1 Venn, 1 sample-space grid |
| 6-8 | Multiplication theorem and independent events | 2 tree diagrams |
| 9-11 | Total probability theorem, partition of sample space | 1 partition Venn, 1 tree |
| 12-14 | Bayes' theorem, posterior-probability problem | 2 Bayes trees, 1 solved factory-defect problem |
| 15-17 | Random variable, probability distribution, mean and variance | 1 distribution table, 1 expectation table |
| 18-19 | Bernoulli trial, binomial distribution B(n,p) | 1 binomial probability table (n=1 to 6) |
Hand-drawn diagram inventory for Class 12 Probability
Every diagram below sits inside the scanned PDF on the page noted. The inventory makes the diagrams searchable so you can flip directly to the visual you need during revision.
| Diagram | Page | What it shows |
|---|---|---|
| Venn 1: A and B in sample space S | 1 | Visual definition of P(A), P(B), P(A and B) |
| Venn 2: mutually exclusive vs independent | 2 | Side-by-side contrast (often confused) |
| Venn 3: conditional probability shading | 3 | Shaded region for P(A|B) inside B |
| Sample-space grid: two dice | 5 | 36-cell grid with favourable outcomes circled |
| Tree 1: independent coin tosses | 6 | Two-stage branching with 1/2 labels |
| Tree 2: drawing without replacement | 8 | Conditional probabilities on branches |
| Partition Venn: E1, E2, E3 with event A | 9 | Total probability theorem geometry |
| Bayes tree: medical-test problem | 12 | Disease vs healthy branches, false-positive arm |
| Bayes tree: bag-of-balls problem | 13 | Two-bag posterior probability |
| Distribution table: X = number of heads in 3 tosses | 15 | Hand-drawn X / P(X) two-row table |
| Binomial table: B(n,p) for n=1 to 6 | 18 | P(X=r) values for ready reference |
Full formula reference: Probability Formula Sheet Class 12 Maths.
Conditional probability and Bayes solved by hand
The hardest jump in the Probability and Statistics Handwritten Notes is going from a worded Bayes problem to the right tree. The notebook walks through one full example on pages 12 to 13 so the procedure is fixed before you attempt CBSE-style questions.
Solved problem (page 12, full handwriting in PDF): A factory has two machines, M1 and M2, producing 60% and 40% of the output. The defect rates are 3% and 5%. A randomly selected item is found defective. Find the probability it came from M2.
Step 1. Draw the tree. First level: P(M1) = 0.6, P(M2) = 0.4. Second level: defect arm P(D|M1) = 0.03, P(D|M2) = 0.05.
Step 2. Total probability of defect:
P(D) = P(M1)P(D|M1) + P(M2)P(D|M2) = 0.6 × 0.03 + 0.4 × 0.05 = 0.018 + 0.020 = 0.038 .
Step 3. Apply Bayes:
P(M2|D) = P(M2)P(D|M2)P(D) = 0.0200.038 ≈ 0.5263 .
So the defective item is roughly 52.6% likely to have come from M2, even though M2 produces only 40% of the output. This counter-intuitive result is the whole point of Bayes' Theorem.
Binomial distribution quick-reference table
The binomial table on page 18 of the notebook gives P(X = r) for B(n, p) with n from 1 to 6. It is the single fastest way to verify a binomial answer in the exam without redoing the full nr pr (1-p)n-r calculation. A condensed version is below; the full hand-drawn table sits in the Probability and Statistics Handwritten Notes.
| n | Formula for P(X = r) | Mean (np) | Variance (npq) |
|---|---|---|---|
| 1 | pr q1-r , r = 0, 1 | p | pq |
| 2 | 2r pr q2-r | 2p | 2pq |
| 3 | 3r pr q3-r | 3p | 3pq |
| 4 | 4r pr q4-r | 4p | 4pq |
| 5 | 5r pr q5-r | 5p | 5pq |
| 6 | 6r pr q6-r | 6p | 6pq |
Here q = 1 - p. The mean and variance columns are worth memorising; CBSE has set direct one-mark questions on them.
Last 24-hour revision card for Probability
Use the night before the board exam. Skim these in order; do not reopen the full PDF.
- One-line formula recall: P(A|B) = P(A ∩ B)P(B) , P(A ∩ B) = P(A) P(B|A) , Bayes' P(Ei|A) = P(Ei)P(A|Ei)∑ P(Ej)P(A|Ej) .
- Independent vs mutually exclusive: independent means P(A ∩ B) = P(A)P(B) ; mutually exclusive means P(A ∩ B) = 0 . The two are NOT the same.
- Random variable checklist: mean = ∑ xi P(xi) , variance = ∑ xi2 P(xi) - μ2 .
- Binomial flag: identical trials, two outcomes, fixed p, independence. If any fail, it is not binomial.
- Common trap: "at least one" problems use 1 - P(none) . Going direct almost always wastes time.
Memory mnemonics for Probability concepts
- "CIA" for conditional probability sequence: Condition, Intersect, Apply formula. Read the worded "given that" clause first (Condition), then write the intersection (Intersect), then divide (Apply).
- "PIE" for Bayes' Theorem branches: Prior, Intermediate (the likelihood), Evidence (the marginal). Posterior = Prior multiplied by Likelihood, divided by Evidence.
- "BIN" for binomial conditions: Bernoulli trial, Independence, N fixed. If all three hold, B(n, p) applies.
- "MV ratio = q": for any binomial, variance divided by mean equals q. Useful sanity check in 1-mark MCQs.
How will Collegedunia's Handwritten Probability Notes help you?
- Exam-hall handwriting model: the notebook is written in the exact pen style and step sequence CBSE examiners expect, so you internalise the format while revising.
- Diagram-led learning: 12 hand-drawn visuals replace 12 dense paragraphs of typeset notes. The Bayes tree on page 12 alone covers two recurring CBSE problem types.
- Built for the 24-hour window: the 19-page count is sized so the entire chapter can be revised in one focused 90-minute session.
- Aligned to 2026-27 NCERT: nothing in the notebook references topics that NCERT has dropped from the current edition.
Related Resources for Class 12 Maths Chapter 13
- NCERT Solutions for Class 12 Maths Chapter 13 Probability
- Class 12 Maths Chapter 13 Probability Notes
- Probability Formula Sheet Class 12 Maths
- NCERT Exemplar Solutions for Class 12 Maths Chapter 13
Frequently Asked Questions on Class 12 Maths Probability Handwritten Notes
Probability and Statistics Handwritten 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.
| Exercise | Topic Tested |
|---|---|
| Exercise 13.1 | Conditional probability |
| Exercise 13.2 | Multiplication theorem; independence of events |
| Exercise 13.3 | Bayes' theorem and total probability |
| Miscellaneous Exercise | Mixed probability problems |
PDF Download Formats and Languages for the Probability Chapter
The Probability Class 12 PDF 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:
| Format | Best for | Approx. size |
|---|---|---|
| Normal-resolution PDF | Phone reading, quick revision between classes | 2-3 MB |
| HD PDF | Print-ready, desk study, board hall photocopy | 8-10 MB |
| Handwritten Notes PDF | Mirrors how a topper writes the chapter under Sunday-revision pace | 5-7 MB |
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 probability class 12 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 probability class 12 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:
| Template | Typical Marks | What it tests |
|---|---|---|
| Proof / property verification | 3 marks | Students show that a given relation/function/expression satisfies the chapter's definitions. |
| One-step computation | 2 marks | Substitution-based item: plug into a known formula and simplify. |
| Case-study scenario | 4 marks | Real-world setup applying the chapter's definitions, introduced in CBSE 2021+ papers. |
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.
- probability class 12 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 this chapter 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:
| Year | Dominant Question Type | Approx. Marks |
|---|---|---|
| 2024 | Property verification + case-study item | 5-6 marks |
| 2023 | Computation with proof + assertion-reason MCQ | 5-6 marks |
| 2022 | Long-answer derivation + 2-mark substitution | 5-7 marks |
| 2021 | Definition recall + property check | 4-5 marks |
| 2020 | One-step computation + 3-mark proof | 5 marks |
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:
| Resource | Use it for | When |
|---|---|---|
| Probability Notes (this page) | Theory, definitions, exam patterns | First pass, before practice |
| these notes ncert solutions PDF | Step-by-step solved exercises | Second pass, during NCERT practice |
| probability class 12 formulas PDF | One-page identity recall | Third pass, alongside mock papers |
| Handwritten Notes PDF | Quick reading in topper's handwriting | Anytime, especially commute revision |
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 Class 12 page ncert solutions cover every back-of-chapter exercise plus the miscellaneous exercise.
- The probability class 12 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 the resource 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:
| Reference | How it maps to the chapter notes |
|---|---|
| RD Sharma Class 12 Probability | Question patterns overlap with NCERT at ~70%; an advanced supplement. |
| ML Aggarwal Class 12 Probability | Solutions style is closer to JEE; good for problem-solving practice. |
| Teachoo probability class 12 | Free online walkthroughs; useful for video-style learning. |
| Shaalaa probability class 12 solutions | State-board (Maharashtra HSC) phrasings; same core definitions. |
| Maharashtra board the PDF textbook PDF | Same chapter content under the HSC syllabus; exercise numbers differ. |
| NCERT Exemplar Class 12 Probability | Advanced problems for JEE Main/JEE Advanced preparation. |
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:
| Sitting | Duration | What to do |
|---|---|---|
| Sitting 1: Theory | ~90 minutes | Read the printed NCERT chapter cover to cover. Mark every definition and theorem statement. Then read the formula recall section on this page. |
| Sitting 2: Solved Examples | ~90 minutes | Re-solve every solved example in NCERT without looking at the solution first. Compare your steps against the printed working. Use these notes ncert solutions PDF if stuck. |
| Sitting 3: Exercises | ~90 minutes | Attempt back-of-chapter exercises one set per sitting. Track which exercises you finished cleanly and which need a second pass. Click into the linked exercise pages above for verification. |
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.
Frequently Asked Questions
Ques. Are the Probability handwritten notes for Class 12 Maths free to download?
Ans. Yes, the Probability and Statistics Handwritten Notes is free for personal study use. Print on A4 or read on tablet.
Ques. How are these handwritten notes different from typeset NCERT notes?
Ans. The content matches Collegedunia's typeset Notes, but the format is a scanned notebook in pen on ruled paper. Many students find the handwritten layout faster to revise from because it matches the way answers are written in the board exam.
Ques. Do the Probability and Statistics Handwritten Notes cover Bayes' theorem with solved examples?
Ans. Yes. Pages 12 to 14 carry two fully solved Bayes problems (factory-defect and bag-of-balls) with hand-drawn tree diagrams and labelled branch probabilities.
Ques. Is the binomial distribution table included?
Ans. Yes. Page 18 has a binomial probability table for B(n, p) covering n = 1 to 6, plus mean (np) and variance (npq) columns.
Ques. Are these Probability and Statistics Handwritten Notes aligned with the 2026-27 NCERT syllabus?
Ans. Yes, the notebook reflects the current 2026-27 NCERT print of Class 12 Mathematics. No dropped sub-topics are included.
Ques. How many hand-drawn diagrams are inside the Probability and Statistics Handwritten Notes?
Ans. Twelve in total: 7 Venn diagrams (3 sample-space, 4 conditional), 5 tree diagrams (2 independent, 2 Bayes, 1 without replacement), plus a binomial table and a probability distribution table.
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