The Probability Class 12 Exemplar Solutions 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.
| Total Exemplar problems | ~40 (MCQ + MCQ-II + Fill + VSA + SA + LA) |
| JEE Main 2025 hit-rate | 1 question per shift on Bayes or Binomial |
| CBSE 2026-27 weight | 8 marks (Unit VI: Probability) |
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.
Compiled by Collegedunia subject specialists against the 2026-27 NCERT Exemplar print, the latest CBSE 2025 board paper and the JEE Main 2025 January plus April sessions.
Also Check:
- Probability Class 12 Maths NCERT Exemplar Book PDF
- these notes Maths NCERT Solutions
- the PDF Maths Formula Sheet
Problem-Type Split in the Exemplar Class 12 Maths Solutions Chapter 13 Probability
The Exemplar bundles its roughly 40 problems across six formats. Tracking the split helps you allocate practice time: MCQ-II and LA are the slow burners, while VSA and Fill in the Blanks are the quick warm-ups before a CBSE pre-board.
| Problem Type | Approx. Count | What it tests |
|---|---|---|
| MCQ (single correct) | 17 | Direct conditional probability, independence, Bayes |
| MCQ-II (multiple correct) | 2 | Mutual independence vs pairwise; mixed binomial cases |
| Fill in the Blanks | 5 | P(A|B), variance, mean of binomial |
| VSA (Very Short Answer) | 6 | Single-step probability tree, complementary events |
| SA (Short Answer) | 5 | Bayes posterior, expectation of a random variable |
| LA (Long Answer) | 5 | Multi-stage Bayes, binomial parameter fitting |
In CBSE 2025, two of the five 4-mark questions from the this chapter Exemplar Solutions were near-verbatim Exemplar LA problems.
Probability NCERT Exemplar Video Solutions
Source: Magnet Brains on YouTube
Concept Coverage of the Exemplar Probability Solutions PDF
Chapter 13 is part of Unit VI: Probability. The Exemplar drills four concept blocks more aggressively than the main textbook does, and our solutions tag every problem with the block it tests so revision is targeted.
- Conditional probability and the multiplication rule: P(A ∩ B) = P(A) · P(B|A). Used in MCQ Q1 to Q9 and most VSA questions.
- Independence of events: pairwise vs mutual, distinguishing the two through the MCQ-II problems.
- Bayes theorem: P(Ei|A) = P(Ei) P(A|Ei)∑ P(Ej) P(A|Ej) . The single most JEE-cited formula from these notes Exemplar Solutions.
- Random variables and binomial distribution: mean np , variance npq , and the binomial probability mass function P(X = r) = nr pr qn-r .
JEE Main Question Patterns Drawn From the Probability Exemplar
Of the four to six probability questions JEE Main asked across 2024 and 2025, almost every Bayes and binomial question traces back to an Exemplar archetype. The table below maps the dominant patterns latest first.
| Year | Pattern from Exemplar | Exemplar Reference |
|---|---|---|
| JEE Main 2025 | Bayes with three urns, posterior calculation | SA Q26 |
| JEE Main 2024 | Binomial mean and variance, find n and p | LA Q31 |
| JEE Main 2023 | Independence of three events | MCQ-II Q21 |
| JEE Main 2022 | Conditional probability with conditional tree | SA Q24 |
| CBSE 2025 | Bayes with two defective machines | LA Q33 |
Around 70% of Probability questions in JEE Main 2024 and 2025 mapped to an Exemplar Bayes or binomial archetype.
Common Mistakes the Exemplar Class 12 Maths Solutions Chapter 13 Probability Flags
Tip callouts in the this Class 12 page Exemplar Solutions call out five recurring traps. These are the same five that account for most lost marks in CBSE and JEE Main probability sections.
- Reversing the conditional: solving for P(A|B) when the question wants P(B|A). Always rewrite the conditional in symbols before computing.
- Treating pairwise independence as mutual: three events can be pairwise independent yet not mutually independent. The Exemplar MCQ-II problems test exactly this.
- Forgetting binomial trial conditions: trials must be independent and have a fixed success probability. A question about drawing without replacement is NOT binomial.
- Dropping priors in Bayes: P(E_i) must appear in both the numerator and the denominator.
- Mean and variance mix-up: variance is npq, NOT np.
Top Formulas From the Probability Exemplar (Quick Recall)
Five formulas account for almost every Exemplar problem. The full list with derivations lives on the the resource Exemplar Solutions formula sheet, but these five are the ones to lock in before solving the Exemplar.
| Conditional probability | P(A|B) = P(A ∩ B)P(B) |
| Multiplication rule | P(A ∩ B) = P(A) P(B|A) |
| Bayes theorem | P(Ei|A) = P(Ei) P(A|Ei)j P(Ej) P(A|Ej) |
| Binomial PMF | P(X = r) = nr pr qn-r |
| Binomial mean and variance | Mean = np, Variance = npq |
Full PYQ map: the chapter notes Maths Formula Sheet
How Collegedunia's Exemplar Solutions Will Help You
The Probability Exemplar is dense, and a flat answer key does not help in a timed setting. Collegedunia's PDF tags every problem by type, lists the Concept Used up front, and adds an Expert Solution next to each main solution.
That structure mirrors the way a JEE Main aspirant scans during revision, and the way a CBSE student double-checks a 4-mark working two days before the board.
Other Resources
- the PDF Maths NCERT Solutions
- this chapter Maths Notes
- these notes Maths Formula Sheet
- this Class 12 page Maths NCERT Exemplar Book PDF
- the resource Maths Handwritten Notes
NCERT Exemplar Solutions for Class 12 Maths: All Chapters
The table below summarises the recent CBSE Class 12 pattern for this chapter and is a quick pre-exam reference.
| Chapter | Exemplar Solutions |
|---|---|
| Chapter 13 | Probability Exemplar Solutions |
| Chapter 1 | Relations and Functions Exemplar Solutions |
| Chapter 2 | Inverse Trigonometric Functions Exemplar Solutions |
| Chapter 3 | Matrices Exemplar Solutions |
| Chapter 4 | Determinants Exemplar Solutions |
| Chapter 5 | Continuity and Differentiability Exemplar Solutions |
| Chapter 6 | Application of Derivatives Exemplar Solutions |
| Chapter 7 | Integrals Exemplar Solutions |
| Chapter 8 | Application of Integrals Exemplar Solutions |
| Chapter 9 | Differential Equations Exemplar Solutions |
| Chapter 10 | Vector Algebra Exemplar Solutions |
| Chapter 11 | Three Dimensional Geometry Exemplar Solutions |
| Chapter 12 | Linear Programming Exemplar Solutions |
the chapter notes Exemplar Solutions: 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 Exemplar Solutions - Frequently Asked Questions
Ques. How is the NCERT Exemplar Class 12 Maths Chapter 13 different from the main textbook?
Ans. The Exemplar contains around 40 harder problems across MCQ, MCQ-II, Fill in the Blanks, VSA, SA and LA formats, and drills Bayes theorem and binomial distribution well beyond the this chapter Exemplar Solutions's exercise set.
Ques. Are these Exemplar Solutions for Probability free to download?
Ans. Yes, the Exemplar Solutions PDF for Chapter 13 Probability is free to download in line with the 2026-27 NCERT print.
Ques. Which Probability topics are most asked in JEE Main from the Exemplar?
Ans. Bayes theorem and binomial distribution cover. Across JEE Main 2024 and 2025, almost every Probability question in the paper traced back to an Exemplar SA or LA archetype.
Ques. Does these notes Exemplar Solutions cover MCQ-II (multiple correct) Exemplar problems?
Ans. Yes, the two MCQ-II problems on independence of three events are solved in full, with each option evaluated separately.
Ques. Are alternate methods given for the Bayes problems?
Ans. Every Bayes problem includes an Expert Solution that solves it using a tree diagram, which is typically 60 to 90 seconds faster than the formula approach.
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