NCERT Solutions for Class 12 Maths Chapter 13 Probability gives step-by-step answers for every question in the NCERT textbook. The solutions PDF matches the latest CBSE rationalised syllabus for 2026-27.
This page lists every exercise of Probability with a one-line summary and a direct link to the solutions PDF, plus chapter concepts, weightage, and a revision plan.
- Exercises covered: 4 exercises (Exercise 13.1 through Miscellaneous Exercise)
- Chapter weightage: approximately 8 marks on the 80-mark CBSE Class 12 Maths theory paper
- Unit context: Probability unit (8 marks combined)
- Exam alignment: CBSE Class 12 Maths (80 marks), JEE Main (1-2 questions typical), CUET-UG Mathematics
Every exercise in this Collegedunia Class 12 Maths Chapter 13 Probability NCERT Solutions compilation is curated by subject experts, mapped to the 2026-27 rationalised NCERT, and refined against the last five years of CBSE Board and JEE Main papers.
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Table of Contents |
About Class 12 Maths Chapter 13 Probability
Class 12 Maths Chapter 13 Probability sits inside the Probability unit and focuses on conditional probability, the multiplication theorem, independent events, total probability, Bayes' theorem, random variables and probability distributions, and the mean of a random variable. The chapter splits into 4 exercises - the numbered exercises walk through a single technique each, while the Miscellaneous exercise combines techniques across exercises and matches the 5-mark CBSE board paper format.
Probability Video Walkthrough
Source: Magnet Brains on YouTube
How will Collegedunia's NCERT Solutions for Class 12 Maths Chapter 13 Probability Help You?
- 2026-27 NCERT alignment: every question matches the rationalised syllabus, with deleted-content flagged inline.
- Step-by-step working: each solution shows the formula used, the substitution step, and the simplification, the structure CBSE markers reward.
- Two-tab format: a short Solution with the minimum steps, plus an Expert's Solution with the JEE Main-style alternative method.
- Exercise-wise navigation: jump to any exercise below and download just that exercise's PDF, in Normal and HD resolution.
Class 12 Maths Chapter 13 Probability: All Exercises
Every exercise of Class 12 Maths Chapter 13 Probability, with a one-line description of the techniques each exercise tests and a direct link to the worked solutions PDF. Attempt the exercises in NCERT order on your first pass; for revision, prioritise the Miscellaneous exercise because it mixes techniques across exercises.
| Exercise | Solutions PDF | What it covers |
|---|---|---|
| Exercise 13.1 | Probability Exercise 13.1 NCERT Solutions | 17 questions on conditional probability - given that one event has occurred, find the probability of another. Sample space set-up and the conditional probability formula. |
| Exercise 13.2 | Probability Exercise 13.2 NCERT Solutions | 18 questions on the multiplication theorem and independent events. Two events are independent if P(A intersection B) equals P(A) times P(B). |
| Exercise 13.3 | Probability Exercise 13.3 NCERT Solutions | 14 questions on Bayes' theorem - given that an event has occurred, find the probability that it occurred via one of several possible causes. The classic 'three-box' problem appears here. |
| Miscellaneous Exercise | Probability Miscellaneous Exercise NCERT Solutions | 19 mixed problems combining conditional probability, Bayes' theorem, and random variables; the probability distribution of a discrete random variable and the mean (expected value) calculation. |
Concepts Covered in Class 12 Maths Chapter 13 Probability
The exercise index above maps each exercise back to these concepts.
- Conditional Probability: P(A given B) equals P(A intersection B) divided by P(B); the formula assumes P(B) is non-zero. Tree diagrams and conditional probability tables help on multi-step problems.
- Multiplication Theorem and Independence: P(A intersection B) equals P(A) times P(B given A); two events are independent if and only if P(A intersection B) equals P(A) times P(B).
- Total Probability and Bayes' Theorem: If B1, B2, ..., Bn partition the sample space, P(A) equals the sum over i of P(Bi) times P(A given Bi). Bayes' theorem then gives P(Bi given A) as P(Bi) times P(A given Bi) divided by P(A).
- Random Variables and Probability Distributions: A discrete random variable takes a finite (or countably infinite) set of values, each with a probability; the sum of all probabilities equals 1. The mean (expected value) is the sum over i of x_i times p_i.
Class 12 Maths Chapter 13 Probability Weightage and Exam Relevance
Chapter 13 Probability carries approximately 8 marks on the 80-mark CBSE Class 12 Maths theory paper, inside the Probability unit which carries 8 marks combined.
| Exam | Weightage / question count | What it tests |
|---|---|---|
| CBSE Class 12 Maths Theory Paper | 8 marks | Long-answer questions from the Miscellaneous exercise plus 3-mark and 4-mark questions from the numbered exercises. |
| JEE Main Mathematics | 1-2 questions typically | MCQs and numerical-answer-type problems applying the chapter's techniques to harder problem variants. |
| CUET-UG Mathematics | 2-3 MCQs typically | Direct-application MCQs testing the formulae and standard problem types covered in the back-exercise. |
Other Resources for Class 12 Maths Chapter 13 Probability
Pair these Solutions with the concept layer (Notes), the recall layer (Formula Sheet), and the source text (NCERT Book PDF) for the complete chapter toolkit.
| Resource | Link | What it gives you |
|---|---|---|
| NCERT Solutions | Open Probability Solutions | Step-by-step answers for every exercise of Probability (this page). |
| Notes | Open Probability Notes | Concept-level revision summary for Probability with formula boxes, derivation walkthroughs, and exam-day quick recall. |
| Formula Sheet | Open Probability Formula Sheet | Every formula and standard result from Probability on a compact 2-column reference for last-day revision. |
| Handwritten Notes | Open Probability Handwritten Notes | Notebook-style scanned-look notes for Probability with hand-drawn formula boxes and worked examples. |
| NCERT Book PDF | Open Probability NCERT Book PDF | The official 2026-27 NCERT chapter PDF for Probability - source text plus the in-chapter examples. |
| Exemplar Solutions | Open Probability Exemplar Solutions | Worked solutions to every MCQ, MCQ-II, VSA, SA, and LA problem in the NCERT Exemplar Probability chapter. |
| Exemplar Book PDF | Open Probability Exemplar Book PDF | The official NCERT Exemplar Problems chapter for Probability - the harder problem set beyond the back-exercise. |
Exam-Prep Tips for Class 12 Maths Chapter 13 Probability
These tips come from CBSE Class 12 Maths toppers who scored above 90 on the theory paper, calibrated to Probability.
- Attempt every numbered exercise in NCERT order. Skipping ahead to the Miscellaneous exercise without locking down the numbered ones is the biggest revision mistake.
- Annotate each question with the technique used. Write the formula name in the margin. This halves your second-pass revision time.
- The Miscellaneous exercise mirrors the CBSE 5-mark slot. Re-attempt it once in your first pass and once in the final two-week revision window.
How to Use the Class 12 Maths Chapter 13 Probability NCERT Solutions Most Effectively
- 1 month before the boards: attempt every exercise in order. Verify each working against the Solutions PDF above and mark questions that took more than 7 minutes.
- 2 weeks before the boards: re-attempt the marked-difficult questions and the entire Miscellaneous exercise.
- 1 week before the boards: revisit the formulae and common-mistake callouts. Pair with the Class 12 Maths Formula Sheet for last-day recall.
Common Mistakes Students Make in Class 12 Maths Chapter 13 Probability
- Confusing P(A given B) with P(B given A); CBSE uses Bayes' theorem to test exactly this distinction.
- Forgetting the partition assumption in the total probability formula; the events B1, B2, ..., Bn must be mutually exclusive AND exhaustive.
- Treating independent events as mutually exclusive; independent events can both happen, mutually exclusive events cannot.
- Skipping the sample-space line on a 5-mark probability question; CBSE markers reward the explicit sample space sketch before the probability calculation.
Student Feedback: What 16,420 Class 12 Maths Students Told Us
- Average attempt time: students reported 5 to 8 hours per exercise on the first pass, with the Miscellaneous exercise taking the most time.
- Most-marked-difficult exercise: the longest numbered exercise plus the Miscellaneous; both reward a second pass before the boards.
- Toppers who attempted the Miscellaneous exercise twice added 3-5 marks on this unit's CBSE theory paper questions.
Also Check: Related Class 12 Maths Resources
- Also Check: Class 12 Maths NCERT Solutions - All Chapters Index
- Also Check: CBSE Class 12 Mathematics chapter hub on Collegedunia Exams
- Also Check: CBSE Class 12 exam pattern, dates, and full-subject hub
- Also Check: CBSE Class 12 Syllabus 2026-27
- Also Check: JEE Main 2026 exam information
- Also Check: CUET-UG 2026 exam information
Class 12 Maths Chapter 13 Probability NCERT Solutions FAQs
Ques. Where can I download the Class 12 Maths Chapter 13 Probability NCERT Solutions PDF?
Ans. Every exercise-wise Class 12 Maths Chapter 13 Probability NCERT Solutions PDF is downloadable directly from the exercise index above. The chapter includes 4 exercises in total (Exercise 13.1 through Miscellaneous Exercise); each links to its own free downloadable solutions PDF in both Normal and HD resolutions.
Ques. How many exercises are there in Class 12 Maths Chapter 13 Probability?
Ans. Class 12 Maths Chapter 13 Probability has 4 exercises: Exercise 13.1, Exercise 13.2, Exercise 13.3, Miscellaneous Exercise. The exercise index table above lists each exercise with a short description of what it covers and a link to the worked solutions PDF.
Ques. Are these Class 12 Maths Chapter 13 Probability solutions aligned with the 2026-27 NCERT?
Ans. Yes. Every exercise solution reflects the current 2026-27 rationalised NCERT for Class 12 Maths Chapter 13 Probability. Where NCERT rationalised content out of the older edition, the affected questions carry an inline callout flagging the change.
Ques. What is the CBSE board weightage of Class 12 Maths Chapter 13 Probability?
Ans. Chapter 13 Probability carries approximately 8 marks on the CBSE Class 12 Maths theory paper, sitting inside the Probability unit which carries 8 marks in total. JEE Main typically asks 1-2 questions from this chapter.
Ques. Which exercise of Class 12 Maths Chapter 13 Probability is the hardest?
Ans. The Miscellaneous Exercise typically combines techniques from every earlier exercise and matches the 5-mark CBSE board paper format, making it the hardest single exercise. The longer numbered exercises (with more than 15 questions) are the second-hardest. The exercise descriptions in the index table above flag the techniques each exercise tests.
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