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CBSE Class 10 Mathematics Chapter 14 Probability Worksheet with Answers

Probability carries 10 marks in the CBSE Class 10 Mathematics board paper, making Chapter 14 one of the highest-scoring topics when fundamentals are clear. This printable worksheet offers structured practice across experimental and theoretical probability, equally likely outcomes, complementary events, and real-world applications. Designed for students aiming at 90+ percentile, it balances foundational MCQs with HOTS-based long answers and a case-study question modelled on the latest CBSE pattern.

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Key takeaways

✓Complete 30+ question worksheet aligned with CBSE 2025 Class 10 Mathematics board exam pattern and NCERT terminology.
✓Covers experimental probability, theoretical probability, and equally likely outcomes with real-world contexts.
✓Five distinct sections from MCQs to HOTS questions plus one case-study question mirror actual board paper structure.
✓Full answer key with step-by-step explanations provided for self-assessment and concept reinforcement.
✓Moderate to challenging difficulty; complete in 90 minutes to simulate board exam time pressure.
✓Printable PDF-ready format ideal for home practice, school assignments, or quick revision before exams.
✓Addresses common misconceptions like confusing experimental and theoretical probability or miscounting equally likely outcomes.

Worksheet Overview and Instructions

This worksheet is structured to mirror the 2025 CBSE Class 10 board exam pattern for Chapter 14 Probability. Difficulty level is moderate to challenging, targeting students who have completed the NCERT textbook exercises at least once. The suggested time limit is 90 minutes under exam conditions—allocate 20 minutes to Section A and B, 15 minutes to Section C, 25 minutes to Section D, and 30 minutes to Section E and the case-study question. Attempt all questions in sequence. Use a pencil for rough work and pen for final answers. Scientific calculators are permitted, but show all working steps. After completion, refer to the detailed answer key provided at the end to self-assess and identify weak areas. This worksheet is printable; download and solve on paper for the best exam simulation experience.

Total questions: 30+ across five sections plus one case-study
Marks distribution: MCQs (1 mark each), Short answers (2 marks each), Long answers (3 marks each), Case-study (4 marks)
Time limit: 90 minutes (strict exam conditions recommended)
Difficulty: Moderate to challenging, suitable for 85%+ target scorers
Materials needed: Pen, pencil, eraser, scientific calculator, rough paper

Quick Chapter Recap: Probability Fundamentals

Before starting the worksheet, revisit these core concepts from NCERT Class 10 Mathematics Chapter 14. Probability measures the likelihood of an event occurring and ranges from 0 (impossible event) to 1 (certain event). Experimental probability is calculated by dividing the number of trials in which an event occurs by the total number of trials conducted. Theoretical probability assumes equally likely outcomes and is the ratio of favourable outcomes to total possible outcomes. For a single event E, P(E) = Number of favourable outcomes / Total number of outcomes. The probability of an event NOT happening (complementary event) is P(not E) = 1 − P(E). A pack of 52 playing cards has 4 suits (spades, hearts, diamonds, clubs), each with 13 cards (Ace through King). When tossing a fair coin or rolling an unbiased die, all outcomes are equally likely. Understanding these definitions and standard examples is essential before tackling the worksheet questions below.

Experimental probability: Based on actual trials and observations, varies with repetition
Theoretical probability: Based on reasoning and equally likely outcomes, remains constant
Equally likely outcomes: Each outcome has the same chance of occurring (e.g. fair coin, unbiased die)
Complementary events: P(E) + P(not E) = 1 for any event E
Standard setups: 52-card deck, 6-sided die, 2-sided coin, coloured balls in a bag

Section A: Multiple Choice Questions (1 mark each)

This section contains 6 multiple-choice questions testing foundational concepts, definitions, and simple probability calculations. Each question has four options; choose the single correct answer. Read each question carefully—some options are designed to trap common errors like confusing experimental with theoretical probability or misidentifying equally likely outcomes. Show no working for MCQs, but jot rough calculations on scrap paper if needed. Each correct answer earns 1 mark; no negative marking applies. These questions mirror the objective-type items that appear in Section A of the CBSE board paper.

Section B: Fill in the Blanks (1 mark each)

Complete each statement by filling the blank with the correct term, number, or expression. Section B tests recall of definitions, formulas, and standard probability values. Write your answer clearly in the space provided. Spelling and exact terminology matter—use NCERT language wherever possible. For numerical answers, simplify fractions to lowest terms unless instructed otherwise. These questions reinforce key vocabulary like 'equally likely outcomes', 'experimental probability', 'complementary event', and standard setups such as dice, coins, and card decks. Attempt all five blanks; each correct answer earns 1 mark.

Section C: True or False Statements (1 mark each)

Read each statement carefully and write 'True' or 'False' next to it. If the statement is false, you may briefly correct it in one sentence for partial credit in classroom settings (though the worksheet awards 1 mark per correct T/F only). This section checks understanding of probability axioms, definitions, and common misconceptions. For example, students often confuse experimental and theoretical probability or believe that past outcomes affect future independent trials. Pay attention to qualifiers like 'always', 'never', 'only', and 'equally likely'. There are 5 statements in total.

Section D: Short Answer Questions (2 marks each)

Answer the following five questions in 2–3 sentences or show clear numerical working. Each question carries 2 marks. Full marks are awarded only when the method is correct and the final answer is accurate. Partial credit (1 mark) may be given for correct setup or reasoning even if the arithmetic is slightly off. Use proper probability notation: write P(event) and express answers as simplified fractions, decimals to two places, or percentages as instructed. These questions test application of basic probability formulas to word problems involving dice, cards, coloured balls, and real-life scenarios. Show all steps: identify total outcomes, count favourable outcomes, then compute the ratio.

Section E: Long Answer and HOTS Questions (3 marks each)

This section contains three long-answer and higher-order thinking questions, each carrying 3 marks. These problems require multi-step reasoning, application of complementary events, or combining probability with other mathematical concepts like arithmetic progressions or geometry. Write detailed solutions with clear justifications. Marks are split as: 1 mark for correct method/setup, 1 mark for intermediate working, and 1 mark for the final accurate answer. HOTS questions may ask you to prove a statement, find unknowns given certain probability conditions, or analyze experimental versus theoretical results. Allocate 8–10 minutes per question in this section.

Case-Study Based Question (4 marks)

Read the following case-study carefully and answer the sub-questions that follow. Case-study questions integrate real-world contexts with probability concepts and have become a staple of CBSE board papers since 2021. This question carries 4 marks in total, split across 3–4 sub-parts. Each sub-part may be worth 1 or 2 marks. Show all working and reasoning. Marks are awarded for correct interpretation of the scenario, accurate identification of favourable and total outcomes, and logical step-by-step calculations. The case-study below involves a school event and ticket draws, a common board exam theme.

Complete Answer Key with Explanations

Below is the complete answer key for all sections of the worksheet. Each answer includes a brief explanation or working so students can verify their method and learn from mistakes. Use this key only after attempting all questions yourself. For MCQs and fill-in-the-blanks, correct answers are provided with one-line reasoning. For short and long answers, step-by-step solutions are shown with key formulas highlighted. Mark your own work honestly, then revisit NCERT examples or CBSE Class 10 Mathematics notes for any topic where you scored less than 70%. Probability becomes intuitive with repeated practice on varied problem types.

Section A answers: Correct option with brief justification for each MCQ
Section B answers: Exact term or simplified numerical answer for each blank
Section C answers: True/False with one-sentence correction if false
Section D answers: Full working with formula, substitution, and final answer
Section E answers: Detailed multi-step solutions for HOTS questions
Case-study answers: Sub-part wise breakdown with marks allocation

Common Mistakes to Avoid in Probability Problems

Students preparing for the CBSE Class 10 Mathematics board exam often make recurring errors in Chapter 14 Probability. First, confusing experimental and theoretical probability: remember that experimental probability depends on actual trials and varies, while theoretical probability is calculated from equally likely outcomes and stays constant. Second, incorrect counting of favourable outcomes—always list outcomes systematically (use a table or tree diagram for two dice or multiple events) to avoid missing or double-counting. Third, failing to simplify fractions: the board marking scheme awards full marks only when the final probability is in simplest form. Fourth, misinterpreting 'at least', 'at most', and 'exactly' in word problems: sketch a quick Venn diagram or number line if needed. Fifth, forgetting that P(E) + P(not E) = 1 is a powerful shortcut for complementary events. Sixth, assuming that past independent trials affect future outcomes (the gambler fallacy). Practice 20–30 varied problems to internalize these patterns and avoid silly mistakes under exam pressure.

Confusing experimental (trial-based) and theoretical (equally likely outcomes) probability definitions
Incorrect counting: missing or double-counting favourable outcomes in multi-step events
Not simplifying final answers; CBSE marking schemes require lowest-term fractions
Misreading 'at least', 'at most', 'exactly'—translate into clear outcome sets before calculating
Ignoring complementary event shortcut: P(not E) = 1 − P(E) saves time in complex problems
Gambler fallacy: believing previous independent results influence next outcome (e.g. coin tosses)

How CBSETUTOR.ai Helps Master Probability

Probability problems become intuitive with guided, on-demand practice—exactly what CBSETUTOR.ai delivers. Students can snap a photo of any worksheet question and receive instant step-by-step solutions that mirror NCERT language and CBSE marking schemes. The AI tutor covers experimental and theoretical probability, equally likely outcomes, complementary events, card-deck problems, dice combinations, and case-study questions. Beyond Chapter 14, the platform offers 24×7 doubt-solving across all Class 10 Mathematics chapters, plus previous years' board papers and topic-wise tests. At a flat ₹999 per month for every class (6–12), it costs less than two hours with a private tutor yet is available around the clock. Parents in smaller towns especially value this: their child gets metro-level coaching without commute stress. A 3-day free trial lets families experience the AI tutor risk-free. When Chapter 14 concepts click through repeated, personalized practice, students often score full marks in the Probability section of the board paper.

Photo-upload solving: snap any probability question, get instant NCERT-style step-by-step solutions
24×7 availability: clarify doubts at 11 PM before the exam, no scheduling needed
Flat ₹999/month for all subjects and classes 6–12; one price, unlimited questions
3-day free trial: test the platform with Chapter 14 problems before committing
Curated practice sets: topic-wise MCQs, short answers, HOTS, and case-studies aligned to latest CBSE pattern
Bridges Tier-2 and Tier-3 coaching gaps: delivers expert-level guidance without metro commute or high fees

Tips for Scoring Full Marks in the Probability Section

To secure all 10 marks from Probability in the CBSE Class 10 board paper, follow these strategic tips. First, memorize standard setups: 52-card deck composition (4 suits, 13 ranks, 12 face cards), 6-sided die outcomes, and coin-toss sample spaces. Second, always write the formula P(E) = (Number of favourable outcomes)/(Total number of outcomes) before substituting numbers—this earns method marks even if your count is off. Third, for two-dice problems, draw a 6×6 grid and mark favourable cells; this visual check prevents counting errors. Fourth, use complementary probability whenever 'not' or 'at least' appears: often P(not E) is easier to compute. Fifth, express final answers as simplified fractions unless the question specifies decimal or percentage. Sixth, in case-study questions, underline key data and restate what is being asked in your own words before solving—this reduces misinterpretation. Seventh, allocate 10–12 minutes in the board exam for the 10-mark Probability section; do not rush. Eighth, after solving, double-check that all probabilities lie between 0 and 1. Finally, solve at least 50 varied problems—mix NCERT examples, exemplar questions, previous years' papers, and worksheets like this one—so you recognize every question type instantly in the exam hall.

Memorize standard setups: 52-card deck, 6-sided die, coin tosses, and coloured balls distributions
Write the formula first: P(E) = favourable/total earns method marks even if final answer is wrong
Use 6×6 grids for two-dice problems to visualize and count outcomes accurately
Leverage complementary events: P(not E) = 1 − P(E) simplifies 'at least' and 'not' questions
Simplify fractions to lowest terms; board marking schemes deduct for unsimplified answers
In case-studies, underline key data and restate the question to avoid misinterpretation
Allocate 10–12 minutes for Probability in the board exam; balance speed with accuracy
Solve 50+ varied problems before the exam to recognize every question pattern instantly

Frequently asked questions

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

Chapter 14 Probability carries 10 marks in the CBSE Class 10 Mathematics board paper. Questions typically include 2 MCQs (2 marks), 1 short-answer question (2 marks), 1 long-answer or case-study question (4–5 marks), making it one of the highest-weightage chapters in the Statistics and Probability unit.

What is the difference between experimental and theoretical probability?+

Experimental probability is calculated by actually performing trials and recording outcomes: number of times event occurs divided by total trials. It varies with repetition. Theoretical probability uses reasoning and equally likely outcomes: number of favourable outcomes divided by total possible outcomes. It remains constant and is the focus of most board exam questions.

How should I prepare Chapter 14 Probability for the board exam?+

First, complete all NCERT textbook exercises and examples to master basic definitions and standard problems. Next, solve NCERT Exemplar and previous years' board papers to see question patterns. Practice 50+ problems covering dice, cards, balls, and case-studies. Focus on complementary events, 'at least'/'at most' phrasing, and multi-step counting. Finally, take timed worksheets like this one to build speed and accuracy under exam conditions.

Can probability values be greater than 1 or negative?+

No. Probability of any event must lie between 0 and 1, inclusive. A probability of 0 means the event is impossible; a probability of 1 means the event is certain. If your calculation yields a value less than 0 or greater than 1, recheck your counting of favourable and total outcomes because an error has occurred.

How do I handle 'at least' and 'at most' in probability questions?+

'At least k' means k or more; 'at most k' means k or fewer. For 'at least' problems, it is often faster to use the complementary event: P(at least 1) = 1 − P(none). For 'at most' problems, add probabilities of all outcomes up to and including k. Always list outcomes clearly to avoid missing any.

What are equally likely outcomes, and why are they important?+

Equally likely outcomes are outcomes that have the same probability of occurring, such as each face of a fair die (1/6 each) or each card in a shuffled deck (1/52 each). Theoretical probability formulas assume equally likely outcomes. If outcomes are not equally likely, you must adjust probabilities or use experimental data instead.

How many questions are in this worksheet and how long should it take?+

This worksheet contains 30+ questions across five sections (MCQs, fill-in-the-blanks, true/false, short answers, long answers) plus one case-study question. The suggested completion time is 90 minutes under strict exam conditions. Allocate time section-wise: 20 min for A and B, 15 min for C, 25 min for D, 30 min for E and case-study.

Do I need to memorize the composition of a 52-card deck?+

Yes. A standard deck has 52 cards in 4 suits: spades, hearts, diamonds, clubs. Each suit has 13 cards: Ace, 2–10, Jack, Queen, King. There are 12 face cards (4 Jacks, 4 Queens, 4 Kings) and 26 red cards (hearts and diamonds), 26 black cards (spades and clubs). Memorizing this saves time and prevents errors in card-based probability questions.

How does CBSETUTOR.ai help with Probability practice?+

CBSETUTOR.ai offers 24×7 AI-powered doubt solving. Snap a photo of any probability problem—MCQ, case-study, or HOTS—and receive instant step-by-step solutions aligned with NCERT language and CBSE marking schemes. At ₹999/month flat for all subjects and classes 6–12, it is more affordable than a single private tutoring session. A 3-day free trial is available so students can test the platform risk-free.

Is this worksheet enough for full board exam preparation in Probability?+

This worksheet is excellent for targeted practice and self-assessment, but combine it with NCERT exercises, NCERT Exemplar problems, previous years' board papers, and sample papers. Aim to solve at least 50 diverse problems before the exam. Use the detailed answer key here to identify weak areas, then revisit those topics in your NCERT textbook or Class 10 Mathematics notes.

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