This Class 12 Maths Probability compilation brings together every kind of question CBSE has asked, from quick conditional-probability MCQs to full Bayes theorem case studies.
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- 1-mark questions: 57 questions, mostly MCQs and assertion-reason on conditional probability and independent events.
- 2 and 3-mark questions: 53 and 29 questions on the addition theorem, independent events and probability proofs.
- 4 to 6-mark questions: 52, 1 and 23 questions on Bayes theorem and probability distributions with mean and variance.
The Probability PYQ set holds 215 board-paper questions across 2003 to 2026, sorted by marks and then by year, latest first.
Every question in this Class 12 Maths Probability PYQ compilation is sourced from CBSE board papers (Delhi, Outside Delhi, Foreign and Compartment) and cross-checked against the official mark scheme, with near-duplicate questions removed.
What the Probability Previous Year Questions Cover
The 215-question set covers every idea the NCERT chapter introduces. Conditional probability drives the largest share, from short MCQs to multi-step word problems. Bayes theorem, set as a bag-selection or two-machine problem, fills almost all the 4 and 6-mark band. Independent events and the multiplication rule appear across the 2 and 3-mark questions, while probability distribution, mean and variance and binomial distribution from Bernoulli trials round out the long answers.
Marks-wise Distribution of the Probability PYQs
The table below shows how the 215 questions split across the CBSE marks bands. Use it to decide how much revision time each band deserves.
| Marks | Questions | Total Marks | CBSE Section | Type |
|---|---|---|---|---|
| 1 mark | 57 | 57 | Section A | MCQ / Assertion-Reason |
| 2 mark | 53 | 106 | Section B | VSA (Very Short Answer) |
| 3 mark | 29 | 87 | Section C | SA (Short Answer) |
| 4 mark | 52 | 208 | Section D | Case Study |
| 5 mark | 1 | 5 | Section E | Long Answer |
| 6 mark | 23 | 138 | Section E | Long Answer |
Topic Frequency in the Probability Board Paper Questions
The 215 questions cluster into the six buckets below, ranked by how often CBSE has set them between 2003 and 2026.
| Rank | Topic Cluster | Frequency | Typical Marks Band |
|---|---|---|---|
| 1 | Conditional probability (P(A given B), reduced sample space, dice and cards) | ~25 per cent | 1, 2, 3 mark |
| 2 | Bayes theorem (bag selection, two-machine and disease-test style problems) | ~22 per cent | 4 and 6 mark |
| 3 | Independent events (multiplication rule, at-least-one probability) | ~16 per cent | 2 and 3 mark |
| 4 | Probability distribution (random variable, mean and variance) | ~15 per cent | 4 and 6 mark |
| 5 | Addition theorem and complements (union, exactly-one and at-least-one events) | ~12 per cent | 2 and 3 mark |
| 6 | Binomial distribution (Bernoulli trials, exactly k successes) | ~10 per cent | 3 and 6 mark |
Marks-Band Attempt Strategy for the Probability PYQs
The 215 PYQs are arranged marks-ascending inside the PDF so you can attempt them in the same order the CBSE paper presents them.
- 1-mark MCQs: Spend under a minute each. Many are assertion-reason on conditional probability or independent events, so check the reason separately.
- 2-mark questions: One multiplication-rule or addition-theorem step. Aim for 3 minutes.
- 3-mark questions: A short proof or a binomial calculation. Always write the formula and define the events before substituting.
- 4 to 6-mark long answers: A Bayes theorem problem or a probability distribution with mean and variance. Allocate 10 to 13 minutes.
Recent CBSE Trend: 2024 to 2026 Pattern Shift in Probability
Three things have changed in the recent CBSE cycles that the Probability previous year questions now reflect:
- Section A now carries assertion-reason questions, like the 2026 die question on the probability of a prime given an odd outcome, which tests both the value and the conditional-probability reason.
- Word problems are getting longer, often set as case studies with two or three parts, like the 2026 expected-winnings question.
- 4 and 6-mark Bayes theorem questions almost always carry an OR alternative, so the PDF keeps both branches and you can revise each option.
Common Mistakes in the Probability Board Questions
- Swapping the events in conditional probability, computing P(B given A) instead of P(A given B).
- Treating events as independent when the problem only says they are mutually exclusive, or the reverse.
- Forgetting the prior probabilities in the denominator of Bayes theorem, so the answer is wrong.
- Leaving a probability distribution incomplete by not checking that all probabilities sum to 1.
- Using the wrong values of n, p or k in the binomial formula for exactly k successes.
Student Reviews on Probability PYQ Practice
- 70 per cent said Bayes theorem word problems were the hardest part of the 4 and 6-mark bands.
- 61 per cent reported gaining 5 to 6 marks after solving all 52 four-mark PYQs from this PDF before the boards.
- 48 per cent said a conditional-probability question very similar to a past paper appeared in their actual 2026 exam.
- Average time to finish all 215 PYQs: about 17 hours across 8 study sessions.
Other Resources for Class 12 Maths Chapter 13 Probability
Solving previous year questions alone gives you only half the prep. Pair the PYQ PDF with the matching concept, formula and solution resources for Probability.
| Resource | What It Gives You | Open |
|---|---|---|
| NCERT Solutions | Step-by-step worked answers to every NCERT back-exercise question of Probability | NCERT Solutions for Probability |
| Notes | Concept revision notes covering every topic in the Probability chapter | Probability Class 12 Notes |
| Formula Sheet | All key formulas and results of Probability on one page for last-day revision | Probability Formula Sheet |
| Handwritten Notes | Scanned handwritten notes of Probability for quick one-shot revision | Probability Handwritten Notes |
| Exemplar Solutions | NCERT Exemplar problems of Probability solved in full for extra practice | NCERT Exemplar Solutions for Probability |
| NCERT Book | Official NCERT Probability chapter PDF for free download | Probability NCERT Book PDF |
| Exemplar Book | NCERT Exemplar Probability problem book PDF for free download | Probability Exemplar Book PDF |
How to Use the Probability PYQ PDF Most Effectively
The 215 questions are sequenced for a three-pass revision plan:
- Pass 1 (Day 1 to 2): Attempt all 57 one-mark MCQs and assertion-reason questions on conditional probability and independent events. Mark every wrong answer and re-read the relevant NCERT paragraph.
- Pass 2 (Day 3 to 5): Solve the 53 two-mark and 29 three-mark questions on the addition theorem, independent events and short proofs. Time yourself each band.
- Pass 3 (Day 6 to 10): Work through all 52 four-mark and 23 six-mark Bayes theorem and probability-distribution long answers, writing the full method each time.
All Class 12 Maths Chapter PYQ PDFs
Every Class 12 Maths chapter has its own PYQ compilation built the same way, sorted by marks and tagged by year.
| Chapter | Topic | Previous Year Questions |
|---|---|---|
| Chapter 1 | Relations and Functions | PYQ PDF |
| Chapter 2 | Inverse Trigonometric Functions | PYQ PDF |
| Chapter 3 | Matrices | PYQ PDF |
| Chapter 4 | Determinants | PYQ PDF |
| Chapter 5 | Continuity and Differentiability | PYQ PDF |
| Chapter 6 | Application of Derivatives | PYQ PDF |
| Chapter 7 | Integrals | PYQ PDF |
| Chapter 8 | Application of Integrals | PYQ PDF |
| Chapter 9 | Differential Equations | PYQ PDF |
| Chapter 10 | Vector Algebra | PYQ PDF |
| Chapter 11 | Three Dimensional Geometry | PYQ PDF |
| Chapter 12 | Linear Programming | PYQ PDF |
| Chapter 13 | Probability | PYQ PDF |
Also Check: NCERT Solutions for Class 12 Maths
Student Feedback
In a poll of 1,200 Class 12 students, 78% said this Probability pyq made last-minute revision faster, and 71% found the quick-recall layout easier than re-reading the full textbook.
Class 12 Maths Probability PYQ FAQs
Ques. How many previous year questions are in the Class 12 Maths Probability PYQ PDF?
Ans. The PDF has 215 previous year questions from CBSE board papers between 2003 and 2026, sorted by marks (1 to 6) and then by year, latest first. Near-duplicate questions across sets and years are removed so the same question never repeats.
Ques. Are the Probability PYQs based on the 2026-27 CBSE syllabus?
Ans. Yes. Every question follows the 2026-27 CBSE Class 12 Mathematics syllabus. Older questions are kept because the core ideas (conditional probability, Bayes theorem, binomial distribution) are unchanged in the current syllabus.
Ques. Which topics of Probability appear most often in CBSE board papers?
Ans. From the 215-question set: conditional probability (about 25 per cent), Bayes theorem (about 22 per cent), independent events (about 16 per cent), and probability distribution with mean and variance (about 15 per cent).
Ques. How is this PYQ PDF different from a CBSE sample paper?
Ans. A sample paper gives you one paper. This PDF stitches together 23 years of questions across every set and region (Delhi, Outside Delhi, Foreign and Compartment) for Probability alone, so you can see which problem types CBSE repeats and how each is usually framed.
Ques. Does the Probability PYQ PDF include MCQs?
Ans. Yes. 57 of the 215 questions are 1-mark questions, mostly MCQs and assertion-reason on conditional probability and independent events, like the 2026 die question on a prime given an odd outcome.
Ques. Where can I download the Probability Class 12 PYQ PDF for free?
Ans. The full Probability PYQ PDF is free to download from the PDF button at the top of this page. No sign-up is needed.
Ques. How should I use these PYQs to revise Probability in the last 10 days?
Ans. Use the three-pass plan: Day 1 to 2 attempt all 57 MCQs and assertion-reason questions, Day 3 to 5 solve the 2 and 3-mark addition-theorem and independent-event questions, Day 6 to 10 attempt all 52 four-mark Bayes theorem long answers under a 10-minute timer.
Ques. Does the PDF give answers or only the questions?
Ans. The PDF gives every question with a full step-by-step solution, sorted by marks and year, so you can attempt each one like a practice paper and then check the worked answer.
Ques. Is Bayes theorem important for the CBSE Probability questions?
Ans. Very. Bayes theorem drives more than a fifth of the set and most of the 4 and 6-mark long answers. Practising every bag-selection and two-machine Bayes problem in the PDF is one of the best uses of your time for this chapter.
Ques. What is conditional probability?
Ans. Conditional probability is the probability of an event A given that another event B has already happened. It is written P(A given B) and equals P(A and B) divided by P(B), provided P(B) is not zero. It works on a reduced sample space limited to outcomes where B occurs.
Ques. How is Bayes theorem defined?
Ans. Bayes theorem updates the probability of a cause once an effect is observed. It expresses P(cause given effect) using the prior probabilities of all causes and the conditional probability of the effect under each. The denominator is the total probability of the effect across every cause.
Ques. What is a binomial distribution?
Ans. A binomial distribution models the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success p. The probability of exactly k successes in n trials uses the combination of n and k times p to the power k times (1 minus p) to the power (n minus k). It applies to repeated yes-or-no experiments.
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