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Important Questions: CBSE Class 10 Mathematics Chapter 14 Probability

Q: How much time should I spend on Probability questions in the board exam?

Allocate about 10–12 minutes for the entire Probability section (6–8 marks). A 1-mark MCQ should take under 1 minute, a 2-mark question about 2–3 minutes, and a 3-mark question 4–5 minutes. If a case-based question appears, reserve 5–6 minutes. Practice under timed conditions to build speed and accuracy.

Q: Which NCERT exercises are most important for board exam preparation?

NCERT Exercise 14.1 (experimental probability and basic theoretical probability) and Exercise 14.2 (application-based problems with cards, dice, and data) are both crucial. Solve every question in these exercises at least twice. Also review the examples in the chapter as CBSE often adapts these into board questions with minor variations.

Q: How does CBSETUTOR.ai help with Probability doubts?

CBSETUTOR.ai provides a 24×7 AI tutor where you can upload a photo of any Probability question and receive a detailed step-by-step solution instantly. The platform explains each counting step, formula application, and simplification clearly. It costs ₹999/month for all subjects and classes 6–12, with a 3-day free trial. This personalized support helps you master tricky concepts like card problems and case-based questions at your own pace.

Chapter 14 Probability is a high-scoring topic in CBSE Class 10 Mathematics, contributing 6–8 marks every year. The NCERT chapter builds your understanding of experimental and theoretical probability through relatable examples involving coins, dice, playing cards, and real-world data. This question bank presents 15+ board-pattern questions sorted by marks weightage, complete with model answers to help you prepare systematically and score full marks in this chapter.

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Key takeaways

✓Probability chapter typically carries 6–8 marks in CBSE Class 10 Mathematics board exam with questions ranging from 1-mark MCQs to 3-mark application problems.
✓The chapter focuses on two core concepts: experimental probability (based on trials) and theoretical probability (based on equally likely outcomes).
✓Formula to remember: P(E) = Number of favourable outcomes ÷ Total number of possible outcomes; P(E) always lies between 0 and 1.
✓CBSE often tests probability using real-life contexts like cards, dice, coins, or data tables rather than abstract theoretical questions.
✓Case-based questions (4–5 marks) frequently combine probability with data interpretation from tables, graphs, or surveys.
✓Common mistakes include confusing experimental and theoretical probability, incorrect counting of favourable outcomes, and forgetting that sum of all probabilities equals 1.
✓Practice with deck-of-cards questions (52 cards: 26 red, 26 black, 4 suits) is essential as these appear almost every year in CBSE board exams.

Chapter Overview and Marks Weightage in CBSE Board Exam

CBSE Class 10 Mathematics Chapter 14 Probability is part of Unit VI Statistics and Probability, which together carry 11 marks in the board examination. Typically, this chapter alone contributes 6 to 8 marks. The 2024 and 2025 CBSE board papers featured one 1-mark MCQ, one or two 2-mark questions, and one 3-mark question from Probability. Additionally, the Case-Based Question section in Paper-1 (Standard) sometimes includes a 4-mark or 5-mark problem integrating probability with data tables or graphs. The chapter is conceptually straightforward but requires careful reading of the problem, accurate counting of outcomes, and clear application of the probability formula. Understanding the distinction between experimental probability (based on actual trials or surveys) and theoretical probability (based on equally likely outcomes) is critical, as CBSE deliberately tests both concepts.

Typical weightage: 6–8 marks out of 80 in the board exam
Question pattern: 1-mark MCQ, 2-mark short answer, 3-mark application question, and sometimes a 4–5 mark case-based question
Core NCERT topics: experimental probability, theoretical probability, equally likely outcomes, probability of sure and impossible events
Real-world contexts tested: playing cards (52 cards), dice rolls, coin tosses, survey data, and frequency tables

1-Mark Questions: Multiple Choice and Very Short Answer

One-mark questions test your grasp of basic definitions, simple calculations, and direct application of the probability formula. CBSE typically includes one MCQ from Probability in the board paper. These questions are straightforward but require you to read carefully—especially when dealing with playing cards or dice where students sometimes miscount the total or favourable outcomes. Remember that the probability of any event always lies between 0 and 1 inclusive, the probability of a sure event is 1, and the probability of an impossible event is 0. Practice these quick-fire questions to secure easy marks and build confidence for longer questions. Each question below reflects the style seen in recent CBSE papers and NCERT exemplar problems, ensuring you are exam-ready.

2-Mark Questions: Short Answer with Reasoning

Two-mark questions usually require a two-step calculation or a brief explanation along with the numerical answer. CBSE values method marks, so even if your final answer is incorrect, showing clear working—total outcomes, favourable outcomes, and formula application—can earn you partial credit. These questions often involve playing cards, dice, or simple real-life data. Pay close attention to phrases like 'black king', 'non-face card', or 'number less than 3', which restrict the favourable outcomes. Always simplify your fraction answer to lowest terms. Practice writing concise, step-by-step solutions as demonstrated below. The model answers here mirror the CBSE marking scheme style, ensuring you know exactly what examiners expect.

3-Mark Questions: Application and Problem-Solving

Three-mark questions demand a clear method, correct calculations, and often a two-part or multi-step solution. These questions test your ability to apply probability concepts to real-world scenarios or slightly complex counting problems. CBSE often uses contexts like playing cards (where you must know the composition: 52 cards, 4 suits, 13 ranks, 26 red, 26 black, 12 face cards), or survey data presented in a table. Read the question twice to identify all conditions and list outcomes systematically. Show every step: total outcomes, event definition, counting favourable outcomes, applying the formula P(E) = n(E)/n(S), and simplifying. Even if you make an arithmetic slip, clear method steps fetch you 2 out of 3 marks. Practice these thoroughly as they form the backbone of the chapter's board-exam weightage.

Case-Based and 5-Mark Questions

CBSE introduced competency-based case-study questions from 2021 onwards. These 4- or 5-mark questions present a real-life scenario with data in a table, graph, or paragraph, followed by 3–4 sub-questions testing probability calculations. Read the case carefully, extract the data, and answer each sub-question independently. Often the first sub-question is straightforward (1 mark), the next two are 2 marks each, and you may have a choice in the last part. Show all working even for simple steps because partial marks are awarded generously. Case-based questions integrate probability with statistics, so you might calculate experimental probability from frequency data or interpret a pie chart to find outcomes. Practice these to familiarize yourself with the format and time management, as they can be lengthy to read but are highly scoring if approached systematically.

Case-based questions carry 4–5 marks and include 3–4 sub-questions
Read the scenario twice and underline key numerical data
Sub-questions usually ask for different probabilities from the same data set
Write the formula P(E) = favourable/total for every sub-question to secure method marks

How CBSE Frames Questions from This Chapter

CBSE question setters follow a predictable pattern when designing Probability questions. They favour real-world contexts—playing cards, dice, balls in bags, survey data, or student performance tables—over abstract mathematical statements. Questions are designed to test not just formula recall but your ability to read, interpret, count outcomes correctly, and apply reasoning. CBSE deliberately includes questions where total outcomes or favourable outcomes require careful counting, such as 'cards that are neither king nor queen' or 'numbers divisible by both 2 and 3'. Multi-part questions are common, where part (i) is straightforward and part (ii) or (iii) adds a layer of complexity (e.g., 'at least one', 'exactly two', 'neither...nor'). The marking scheme awards marks for method, so even if final answer is wrong due to a calculation slip, you can still earn 60–70% of the marks if your approach is correct. Understanding this helps you focus on clear, step-by-step presentation in the exam.

Playing-card problems appear almost every year; memorize the deck structure (52 cards, 4 suits of 13 each, 26 red, 26 black, 12 face cards)
Questions involving 'at least', 'at most', 'neither...nor', or 'either...or' test logical counting and complement rule P(not E) = 1 - P(E)
CBSE values method marks: always write total outcomes, favourable outcomes, formula, substitution, and simplified answer
Case-based questions integrate probability with data interpretation; practice reading tables and graphs quickly
Negative marking in MCQs does not apply in board exams, but accuracy in counting is crucial to avoid losing easy marks

Common Mistakes Students Make and How to Avoid Them

Even strong students lose marks in Probability due to a handful of recurring errors. The most frequent mistake is confusing experimental probability (based on actual trials, e.g., 'in 100 tosses, heads appeared 58 times, so P = 58/100') with theoretical probability (based on equally likely outcomes, e.g., 'for a fair coin, P(heads) = 1/2'). CBSE explicitly tests this distinction, so read the question to see if data from an experiment is given or if you must use the classical definition. Another error is miscounting favourable outcomes, especially with playing cards—students forget that there are only 12 face cards (not 16) or count red queens twice when calculating 'red or queen'. Always list outcomes when in doubt. A third mistake is forgetting to simplify fractions; examiners often deduct half a mark for unsimplified answers. Finally, students sometimes write probability greater than 1 or negative, which is impossible—always cross-check that 0 ≤ P(E) ≤ 1. Writing clear step-by-step solutions reduces these errors and earns method marks even if the final answer slips.

Confusing experimental and theoretical probability: read whether the question provides trial data or asks for equally likely outcomes
Miscounting total or favourable outcomes in card/dice problems: list outcomes systematically or use a tree diagram for complex cases
Not simplifying fractions to lowest terms: always reduce your final answer (e.g., 4/52 = 1/13)
Forgetting the complement rule: P(not E) = 1 - P(E) is often faster than counting 'not E' outcomes directly
Arithmetic slips in multi-part questions: double-check addition/subtraction of frequencies or outcomes
Writing probability > 1 or negative: if your answer violates 0 ≤ P ≤ 1, recheck your counting immediately

Additional Practice Questions (Mixed Difficulty)

To consolidate your understanding and build exam confidence, attempt these additional questions covering the full spectrum of difficulty. These questions mirror the variety you will see in the CBSE board paper and include both numerical and conceptual elements. Time yourself—aim to solve a 1-mark question in under 1 minute, a 2-mark question in 2–3 minutes, and a 3-mark question in 4–5 minutes. After solving, compare your method with the model answers below. If you make a mistake, revisit the relevant NCERT section (experimental probability in Section 14.1, theoretical probability in Section 14.2) and work through the examples again. Consistent practice with these question types will help you internalize the counting techniques and probability formula, ensuring you can tackle any variation CBSE throws at you in the board exam.

Leveraging CBSETUTOR.ai for Personalized Probability Practice

While this question bank gives you a solid foundation, every student learns at a different pace and stumbles on different concepts. Some find playing-card problems tricky, others struggle with case-based data interpretation. CBSETUTOR.ai offers a 24×7 AI tutor that adapts to your unique needs. Simply snap a photo of any Probability question—from NCERT, your school worksheet, or a previous year paper—and receive a step-by-step solution with clear explanations of each counting step and formula application. The platform covers all CBSE classes (6 to 12) at a flat ₹999 per month, so whether you need help in Maths, Science, or any other subject, one subscription supports your entire learning journey. Parents appreciate the transparent pricing and the ability to monitor progress, while students love the instant doubt-clearing without waiting for tuition class. Start your 3-day free trial today and experience how personalized AI support can transform your Class 10 board exam preparation, turning probability from a guessing game into a scoring strength.

Photo-upload doubt solving: get instant step-by-step solutions for any Probability question, day or night
Personalized practice: the AI identifies your weak areas (e.g., card problems vs. data-based probability) and suggests targeted questions
Affordable flat pricing: ₹999/month for all subjects, classes 6–12—no hidden costs or per-question charges
3-day free trial: explore the platform risk-free and see how it fits your study routine before committing
Exam-focused content: solutions align with CBSE marking schemes, so you learn exactly how to write answers for maximum marks

Revision Strategy and Last-Minute Tips

With board exams approaching, a focused revision strategy for Probability can secure you 6–8 easy marks. Start by summarizing the key formulae and definitions on a single page: P(E) = n(E)/n(S), P(sure event) = 1, P(impossible event) = 0, P(not E) = 1 - P(E), and the fact that sum of probabilities of all elementary events equals 1. Next, solve all NCERT exercise problems again without looking at solutions—these form the template for board questions. Then tackle the questions in this bank under timed conditions to simulate exam pressure. In the final week, focus on playing-card and case-based questions as these are high-weightage and scoring. On exam day, read each Probability question twice to identify whether it is experimental or theoretical, underline key data, and write every step even if it seems obvious. Examiners reward clear method presentation, and even a small slip in arithmetic will not cost you all the marks if your approach is sound. Stay calm, manage your time (allocate about 10–12 minutes for the entire Probability section), and double-check that all probabilities lie between 0 and 1 before moving on.

One-page formula sheet: write definitions, formulae, and standard results (e.g., deck composition) for quick revision
Solve NCERT Exercise 14.1 and 14.2 completely at least twice before the exam
Practice 10–15 previous year board questions to familiarize yourself with CBSE phrasing and marking patterns
Time yourself: aim to complete the Probability portion in 10–12 minutes during the 3-hour paper
On exam day: read questions carefully, underline data, show all steps, simplify fractions, and verify 0 ≤ P ≤ 1

Frequently asked questions

How many marks does Probability carry in CBSE Class 10 Mathematics board exam?+

Probability typically carries 6 to 8 marks out of 80 in the CBSE Class 10 Mathematics board exam. The question pattern includes one 1-mark MCQ, one or two 2-mark short-answer questions, and one 3-mark application problem. Occasionally a 4–5 mark case-based question also appears.

What is the difference between experimental and theoretical probability?+

Experimental probability is based on actual trials or observed data. For example, if a coin is tossed 100 times and heads appears 58 times, experimental P(heads) = 58/100. Theoretical probability uses equally likely outcomes without conducting experiments; for a fair coin, theoretical P(heads) = 1/2. CBSE tests both, so read the question carefully.

How should I approach playing-card probability questions?+

Memorize the deck structure: 52 cards total, 4 suits (hearts, diamonds, clubs, spades) of 13 cards each, 26 red (hearts + diamonds), 26 black (clubs + spades), and 12 face cards (4 jacks, 4 queens, 4 kings). Always write total outcomes first, then carefully count favourable outcomes based on the question's condition, apply P(E) = favourable/total, and simplify the fraction.

What are common mistakes to avoid in Probability questions?+

Common mistakes include confusing experimental and theoretical probability, miscounting outcomes (especially with cards or 'neither...nor' conditions), not simplifying fractions, double-counting when using 'or' (use n(A∪B) = n(A) + n(B) - n(A∩B)), and writing probabilities outside [0,1]. Always show step-by-step working to earn method marks even if the final answer is incorrect.

How do I solve 'at least one' probability problems quickly?+

Use the complement rule. For 'at least one', it is often easier to calculate P(none) and subtract from 1. For example, when two coins are tossed, P(at least one head) = 1 - P(no heads) = 1 - P(TT) = 1 - 1/4 = 3/4. This saves time compared to listing all favourable outcomes.

What is the weightage of case-based questions in Probability?+

CBSE typically includes one case-based question worth 4 or 5 marks that integrates Probability with data interpretation (tables, graphs, or surveys). These questions have 3–4 sub-parts. They are highly scoring if you read the data carefully and answer each sub-question with clear working. Practice at least 5–6 case-based examples before the exam.

Can probability of an event be greater than 1 or negative?+

No. The probability of any event always lies between 0 and 1, inclusive. P(E) = 0 means the event is impossible, P(E) = 1 means the event is certain, and 0 < P(E) < 1 for all other events. If your calculated answer is negative or greater than 1, recheck your counting of total and favourable outcomes immediately.

How much time should I spend on Probability questions in the board exam?+

Allocate about 10–12 minutes for the entire Probability section (6–8 marks). A 1-mark MCQ should take under 1 minute, a 2-mark question about 2–3 minutes, and a 3-mark question 4–5 minutes. If a case-based question appears, reserve 5–6 minutes. Practice under timed conditions to build speed and accuracy.

Which NCERT exercises are most important for board exam preparation?+

NCERT Exercise 14.1 (experimental probability and basic theoretical probability) and Exercise 14.2 (application-based problems with cards, dice, and data) are both crucial. Solve every question in these exercises at least twice. Also review the examples in the chapter as CBSE often adapts these into board questions with minor variations.

How does CBSETUTOR.ai help with Probability doubts?+

CBSETUTOR.ai provides a 24×7 AI tutor where you can upload a photo of any Probability question and receive a detailed step-by-step solution instantly. The platform explains each counting step, formula application, and simplification clearly. It costs ₹999/month for all subjects and classes 6–12, with a 3-day free trial. This personalized support helps you master tricky concepts like card problems and case-based questions at your own pace.

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