CBSE Class 10 Mathematics Chapter 14 Probability — 20 MCQs with Answers

Experimental probability is derived from actual trials and observations, while theoretical probability rests on the assumption of equally likely outcomes with no bias. NCERT Class 10 defines experimental probability as (number of trials in which event occurred) ÷ (total number of trials). Theoretical probability for an event E is P(E) = (favourable outcomes) ÷ (total outcomes). Many students confuse the two; experimental results converge towards theoretical values as the number of trials increases — this is the law of large numbers. Recognising which formula applies to a given scenario is the first skill tested in MCQs. The questions below isolate this fundamental distinction.

Equally likely outcomes mean each outcome has the same chance of occurring — the foundation of theoretical probability. A fair die, unbiased coin, and well-shuffled deck all satisfy this assumption. NCERT emphasises that if outcomes are not equally likely (e.g. a biased coin), theoretical probability formulae do not directly apply without adjusting weights. Questions in this section test whether you can identify total outcomes, count favourable cases correctly, and simplify fractions. Watch for tricks like 'at least one' or 'exactly two' that require careful counting. These MCQs mirror the 1-mark questions seen in recent CBSE papers.

CBSE loves contextualised questions: defective bulbs in a batch, weather forecasts, sports win-rates. These test whether you can translate a word problem into the probability formula. For instance, 'Out of 500 bulbs, 15 are defective. If one is chosen, what is the probability it is defective?' Answer: 15/500 = 3/100. Real-world scenarios often involve percentages or large numbers; simplify carefully and watch units. The NCERT textbook includes examples from cricket match outcomes and quality-control inspections. The four MCQs here reflect similar contexts and difficulty.

If P(E) is the probability of event E, then P(not E) = 1 − P(E). NCERT Class 10 explicitly states that the sum of the probabilities of all elementary outcomes is 1. This is a favourite testing ground: 'Probability of rain is 0.3; find probability of no rain.' Answer: 0.7. Similarly, 'Probability of passing is 0.85; find probability of failing' gives 0.15. These MCQs are straightforward but require careful reading — students sometimes add instead of subtract. The four questions below drill complementary-event logic and reinforce that 0 ≤ P(E) ≤ 1.

CBSE 2025 papers include 'Assertion (A) and Reason (R)' format: four options — (A) both true and R is correct explanation, (B) both true but R not correct explanation, (C) A true R false, (D) A false R true. Read each statement independently, verify truth, then check logical link. HOTS MCQs demand multi-step reasoning or integration of probability with other topics (e.g. combining probability and statistics). These questions separate top scorers from average ones. The four below are typical HOTS/assertion-reason items seen in recent board papers.

Strategy matters. First, read the question stem carefully — note keywords like 'at least', 'exactly', 'not', 'complementary'. Underline or mentally flag them. Second, identify whether the problem is experimental (given trial data) or theoretical (assume equally likely). Third, write down total outcomes and favourable outcomes in the margin if space permits; this prevents counting errors. Fourth, for assertion-reason, validate A and R separately before deciding the relationship. Fifth, if stuck, use elimination: discard obviously wrong options (e.g. probability > 1 or negative). Sixth, manage time — aim for 30–45 seconds per MCQ; if a question takes longer, mark it and return. Finally, double-check calculations for silly slips like 3/8 read as 3/9. Practicing 20–30 MCQs daily in the fortnight before the exam builds both speed and accuracy. CBSETUTOR.ai offers chapter-wise MCQ quizzes with instant feedback, helping you identify weak areas and track progress over time — all for ₹999/month across Classes 6–12.

Even strong students trip on probability MCQs because the chapter combines logic, arithmetic, and careful reading. Mistake one: confusing experimental and theoretical — using the number of trials as the denominator when the question asks for theoretical probability. Mistake two: forgetting to subtract from 1 for 'not' or complementary events. Mistake three: miscounting favourable outcomes, especially in card or two-dice problems. Mistake four: reading 'at least one' as 'exactly one'. Mistake five: in assertion-reason, picking option (A) without verifying that R actually explains A. Mistake six: skipping simplification and choosing 6/36 when the answer key lists 1/6. Awareness of these pitfalls, combined with regular timed practice, cuts down errors significantly. Reviewing incorrect answers after a mock test is more valuable than doing ten new questions blindly.

Probability consistently appears in CBSE Class 10 board papers with predictable question types: one or two MCQs (1 mark each), often one short-answer (2–3 marks), and occasionally a part in a case-study question. The formulae are few, the logic is transparent, and with 30–40 targeted MCQs you can master the chapter in under a week. Yet many students leave marks on the table due to rushed reading or arithmetic slips. Focused practice under exam conditions is the cure. CBSETUTOR.ai provides an AI tutor available 24×7 that lets you upload a photo of any probability problem — MCQ, word problem, or assertion-reason — and receive a step-by-step solution in seconds. You also get unlimited chapter-wise quizzes, performance analytics, and personalised weak-topic drills. One flat price of ₹999 per month covers every subject and every chapter from Classes 6 to 12, with a risk-free 3-day trial so your child can explore before you commit. For Probability and every NCERT chapter, it is like having a patient tutor on call whenever doubt strikes.