CBSE Class 11 Mathematics Chapter 14 Probability Worksheet with Answers

Chapter 14 in NCERT Class 11 Mathematics establishes the formal framework for probability through random experiments and axiomatic definitions. A random experiment is one whose outcome cannot be predicted with certainty — tossing a coin, rolling a die, or drawing a card from a shuffled deck. The sample space S is the set of all possible outcomes, while an event E is any subset of S. The chapter introduces three axioms: probability of any event lies between 0 and 1; probability of the sample space is 1; for mutually exclusive events, the probability of their union equals the sum of their individual probabilities. Understanding these axioms is crucial because all probability calculations in higher classes and competitive exams rest on this foundation. Students often confuse 'equally likely outcomes' with 'mutually exclusive events' — the former means each outcome has the same chance, while the latter means two events cannot occur simultaneously. Mastery of this chapter requires solving diverse problems on complementary events, exhaustive events, and applying the addition theorem for probabilities.

This section tests your conceptual understanding of probability definitions, axioms, and event classifications. Each MCQ has four options; select the most appropriate answer. These questions are designed at moderate difficulty and reflect the style seen in CBSE Class 11 term exams and board practicals. Remember that the sum of probabilities of all outcomes in a sample space must equal 1, and probability can never be negative or exceed 1. Pay close attention to keywords like 'mutually exclusive', 'exhaustive', and 'complementary'. In the 2024 CBSE Class 11 final exam, about 20 percent of the Probability section carried MCQ-style questions, so this format is essential practice for scoring full marks in objective sections.

Complete each statement with the correct mathematical term or numerical value. These questions reinforce key vocabulary from Chapter 14 of NCERT Class 11 Mathematics and test your recall of definitions and properties. Write your answers clearly. Marks are awarded only for exact terminology as used in the NCERT textbook, so avoid informal language. For instance, write 'mutually exclusive' rather than 'disjoint', even though both are correct in general mathematics usage. This section typically appears in CBSE practical files and internal assessments, and each blank usually carries one mark. Ensure you revise Class 11 Mathematics notes on event types, axioms, and probability calculations before attempting this section. Time allocation for this section should be approximately 10 minutes out of the total 90-minute worksheet duration.

Read each statement carefully and write 'True' or 'False'. Justify your answer in one sentence for full credit. This format tests your ability to distinguish between correct and incorrect applications of probability axioms and event definitions. In CBSE marking schemes, even if you mark the correct True/False, you may lose half a mark if the justification is missing or incorrect. Common traps include confusing 'mutually exclusive' with 'independent' (a topic in Class 12), or assuming that P(A) + P(B) always equals P(A ∪ B) without checking if A and B are mutually exclusive. This section should take about 12 minutes. Write justifications concisely — one line is sufficient. Refer to your Class 11 Mathematics solutions and worked examples if you are unsure about any property during your revision phase before attempting this worksheet.

Answer each question in 2–3 sentences or show clear working for numerical problems. These questions test your ability to apply probability formulas and the axiomatic approach to straightforward problems. Allocate roughly 4 minutes per question, totalling 20 minutes for this section. Marks are split: typically 1 mark for correct method/formula and 1 mark for accurate final answer. Show all steps — even if the arithmetic is simple — because CBSE marking schemes award partial credit for correct process even if the final answer has a calculation slip. Questions in this section mirror Exercise 14.1 and 14.2 from NCERT Class 11 Mathematics and are designed to build fluency in manipulating probability expressions, complementary events, and basic event operations. Use standard notation: P(E) for probability, S for sample space, E' for complement, ∪ for union, ∩ for intersection.

These questions require multi-step reasoning, synthesis of concepts, and clear presentation. Allocate 8–10 minutes per question. Full marks demand complete working with logical flow: state the formula or theorem, substitute values, simplify step-by-step, and box the final answer. HOTS (Higher Order Thinking Skills) questions often combine probability with set theory, counting principles, or real-world modelling. For example, a problem might ask you to first determine the sample space of a compound experiment, classify events, then compute probabilities using axioms and complementary/union rules. In CBSE Class 11 board exams and competitive entrance tests like JEE, such questions differentiate average students from toppers. Always write units or context (e.g., 'probability = 1/3') and double-check that your final probability lies between 0 and 1. Referring to NCERT Class 11 Mathematics solutions for similar problems during revision will build confidence for this section.

Read the scenario below carefully and answer the sub-questions. Case-study questions integrate real-world contexts with mathematical reasoning and have appeared in CBSE sample papers since 2021. Marks distribution: usually 1+1+1+2 across four sub-parts. Write concisely but show key steps. A quality-control engineer at a factory producing LED bulbs selects bulbs at random from a day's production. The factory produces 1000 bulbs daily: 600 white, 250 warm, and 150 RGB bulbs. One bulb is picked at random for inspection. Based on this information, answer: (i) What is the sample space of this experiment? (ii) Find the probability that the selected bulb is white. (iii) Find the probability that the bulb is either warm or RGB. (iv) If the engineer picks a bulb and it is not white, what is the probability it is an RGB bulb? Show all working.

Below are the correct answers and brief explanations for every question on this worksheet. Use this key for self-assessment after completing the worksheet under timed conditions. Award yourself marks honestly and note down topics where you lost marks — those areas need focused revision using your NCERT Class 11 Mathematics textbook and Class 11 Mathematics notes. If you consistently struggle with axiomatic proofs or multi-step problems, consider using CBSETUTOR.ai, where you can upload a photo of any Probability question and receive step-by-step solutions instantly. For just ₹999/month, students in Classes 6–12 get 24×7 access to an AI tutor that explains every step in simple language. Three-day free trial available. Section A: 1(a), 2(b), 3(a), 4(d), 5(b), 6(a). Section B: 7–sample space, 8–mutually exclusive, 9–one, 10–0.9, 11–complement. Section C: 12–True (axiom 1), 13–False (need mutual exclusivity), 14–True (definition), 15–True (P(∅)=0), 16–False (E can be any event with P(E)=1), 17–False (exhaustive means union is S, not intersection). Section D: 18(i) 5/10=1/2, (ii) 8/10=4/5; 19–0.9; 20–S={HH,HT,TH,TT}, P(at least 1 head)=3/4; 21–0.28; 22–6/36=1/6. Section E: 23(i)4/52=1/13, (ii)26/52=1/2, (iii)22/52=11/26; 24–proof uses P(A∪B)=P(A)+P(B)−P(A∩B) and rearrangement; 25(i)3/8, (ii)4/8=1/2, (iii)4/8=1/2. Case study: (i){W,Warm,RGB}, (ii)0.6, (iii)0.4, (iv)150/400=3/8.

Print this page or copy the questions into your notebook. Set a timer for 90 minutes and attempt all sections in one sitting to simulate exam conditions. Do not refer to your NCERT Class 11 Mathematics textbook or Class 11 Mathematics solutions while solving. After time is up, stop and check your answers against the key provided. Award yourself marks: MCQs 1 mark each (6), fill-blanks 1 mark each (5), true/false 1 mark each (6), short answers 2 marks each (10), long answers 4 marks each (12), case study 5 marks — total 44 marks. A score above 35 indicates strong conceptual understanding; 28–34 is satisfactory but requires focused revision on weak areas; below 28 means you should revisit the chapter thoroughly and solve all NCERT exercises again. Identify patterns in your mistakes: are you losing marks in definitions, computational errors, or logical reasoning? Tailor your revision accordingly. For personalized doubt-solving, CBSETUTOR.ai offers an AI tutor available 24×7 at ₹999/month for all classes 6–12 — upload any question photo and get instant, step-by-step explanations. Three-day free trial lets you test the platform risk-free.

Beyond this worksheet, solve all questions in NCERT Class 11 Mathematics Chapter 14 exercises — particularly the miscellaneous exercise at the end, which contains integrative problems. CBSE sample papers and previous years' question papers (available on cbse.nic.in) provide real exam-level difficulty. Many students in metros like Delhi, Mumbai, and Bengaluru rely on expensive coaching for Probability, but self-study with the right resources is equally effective. Make concise notes summarising the three axioms, definitions of event types, and the complement rule on a single page for quick revision. Probability is scoring if you avoid silly mistakes: always verify that your final answer lies between 0 and 1, write fractions in simplest form, and double-check arithmetic. During board exams, Probability questions usually carry 8–10 marks in the Class 11 final paper, so mastering this chapter can significantly boost your overall Mathematics percentage. For students juggling school, tuition, and self-study, CBSETUTOR.ai offers a flat ₹999/month subscription covering Classes 6–12 with unlimited question-solving via photo upload, making premium-quality doubt resolution accessible without the metro-coaching price tag.