Probability — Class 11 MCQs with Answers
Class 11 CBSE Mathematics · Chapter 16
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 11 CBSE Mathematics questions from Chapter 16, "Probability". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE & Maharashtra HSC Board exams, JEE Main, MHT-CET and JEE Advanced apart.
To score well in "Probability", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Probability, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 11 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Key concepts: Probability (Class 11 Mathematics)
This chapter puts chance on a firm axiomatic footing. Starting from random experiments, sample spaces and events as subsets of outcomes, it lays down the axioms of probability, recovers the classical favourable-over-total rule for equally likely outcomes, and proves the addition theorem for the union of two events.
- Random experiment
- An experiment whose set of possible outcomes is known but whose actual outcome cannot be predicted in advance, such as tossing a coin.
- Sample space
- The set S of every possible outcome of a random experiment; each individual outcome in S is called a sample point.
- Event
- Any subset of the sample space; an event occurs when the actual outcome of the experiment belongs to that subset.
- Simple and compound events
- A simple (elementary) event has a single sample point; a compound event contains two or more sample points of S.
Probability — important questions & MCQs with answers (Class 11 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.
- Q1Easy
Probability of head on a fair coin:
A.1/4B.1C.1/2✓ CorrectD.0Answer: C. 1/2
Explanation: A fair coin has 2 equally likely outcomes, so P(head) = 1/2. Picking 1/4 comes from wrongly treating this as a two-coin toss with 4 outcomes instead of one coin with 2.
- Q2Easy
Probability P(A) lies in:
A.RB.[0,1]✓ CorrectC.[−1,1]D.(0,∞)Answer: B. [0,1]
Explanation: Probability is always a value between 0 and 1 inclusive, since it's a fraction of favourable to total outcomes — never negative or above 1. [−1,1] confuses it with a correlation-type range.
- Q3Easy
Sample space S of a random experiment is:
A.Set of all possible outcomes✓ CorrectB.One outcomeC.ProbabilityD.The most likely outcomeAnswer: A. Set of all possible outcomes
Explanation: The sample space S is the set of every possible outcome of a random experiment, e.g. {H,T} for a coin toss — not a single result or a probability value. Mistaking one outcome for the whole space is the usual confusion.
- Q4Easy
An event is:
A.The whole sample space onlyB.Single outcome onlyC.ProbabilityD.A subset of sample space✓ CorrectAnswer: D. A subset of sample space
Explanation: An event is any subset of the sample space — it can be one outcome, several, or the whole space itself, not just a single outcome. Calling it a probability value rather than a set of outcomes is the common mix-up.
- Q5Easy
Classical probability of event E:
A.n(E)·n(S)B.n(S)/n(E)C.n(E)/n(S)✓ CorrectD.1/n(S)Answer: C. n(E)/n(S)
Explanation: Classical probability of event E is P(E) = n(E)/n(S), the count of favourable outcomes over the total outcomes in S. Flipping the ratio to n(S)/n(E) gives a number that can exceed 1, which is never valid.
- Q6Easy
Probability of any event lies in:
A.(0, 1)B.[0, 1]✓ CorrectC.[−1, 1]D.RAnswer: B. [0, 1]
Explanation: Probability of any event satisfies 0 ≤ P(E) ≤ 1, a closed interval including the impossible (0) and sure (1) events. Writing an open interval (0,1) wrongly excludes those two boundary cases.
- Q7Medium
One card is drawn from a well-shuffled deck of 52. The probability that it is a spade is:
A.1/4✓ CorrectB.1/2C.4/13D.1/13Answer: A. 1/4
Explanation: There are 13 spades among the 52 cards.
- Q8Medium
P(not A) =
A.−P(A)B.P(A)C.1 − P(A)✓ CorrectD.P(A)+1Answer: C. 1 − P(A)
Explanation: The complement rule says P(not A) = 1 − P(A), since A and 'not A' together cover the whole sample space and must sum to 1. Writing P(A)+1 instead of subtracting is the common slip.
- Q9Medium
When two dice are thrown together, the number of elements in the sample space is:
A.24B.12C.6D.36✓ CorrectAnswer: D. 36
Explanation: Each die has six outcomes, giving 6 × 6 = 36 ordered pairs.
- Q10Medium
When two coins are tossed, the probability of getting at least one head is:
A.1/4B.1C.3/4✓ CorrectD.1/2Answer: C. 3/4
Explanation: Three of the four outcomes contain a head.
- Q11Medium
If P(A|B) = P(A), then A and B are:
A.Independent✓ CorrectB.Mutually exclusiveC.EqualD.ComplementaryAnswer: A. Independent
Explanation: P(A|B) = P(A) means B's occurrence gives no new information about A, which is exactly the definition of independence. Calling them mutually exclusive is wrong — those events can never occur together, a different property.
- Q12Hard
Two dice rolled — P(sum = 7):
A.6/36 = 1/6✓ CorrectB.1/12C.1/36D.1/2Answer: A. 6/36 = 1/6
Explanation: Two dice give 36 equally likely ordered outcomes, and exactly 6 pairs — (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) — sum to 7, so P(sum=7) = 6/36 = 1/6. Treating the dice as unordered (21 outcomes) is the usual mistake.
- Q13Hard
If A and B are mutually exclusive, P(A∩B) =
A.P(A)+P(B)B.P(A)C.0✓ CorrectD.1Answer: C. 0
Explanation: Mutually exclusive events A and B can never occur together, so their intersection is empty and P(A∩B) = 0. Confusing this with independence, where P(A∩B) = P(A)·P(B) instead, is the chapter's classic trap.
- Q14Hard
When three coins are tossed, the probability of getting exactly two heads is:
A.3/8✓ CorrectB.1/2C.1/4D.1/8Answer: A. 3/8
Explanation: Three of the eight outcomes, HHT, HTH and THH, contain exactly two heads.
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Start this chapter free →Probability — FAQs
What are the key concepts in Class 11 Mathematics Probability?+
This chapter puts chance on a firm axiomatic footing. Starting from random experiments, sample spaces and events as subsets of outcomes, it lays down the axioms of probability, recovers the classical favourable-over-total rule for equally likely outcomes, and proves the addition theorem for the union of two events. Key ideas include Random experiment, Sample space, Event, Simple and compound events.
What does Class 11 Mathematics Chapter 16 (Probability) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Probability": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE & Maharashtra HSC Board exams, JEE Main, MHT-CET and JEE Advanced.
Are these "Probability" questions free to practise?+
Yes. Sign in with Google to practise "Probability" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Probability" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Probability" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to start practising, with instant scoring.
Is there negative marking in the "Probability" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip, the same negative marking as JEE Main and JEE Advanced. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Probability (Class 11 Mathematics)?+
The questions that matter most test Random experiment, Sample space, Event, Simple and compound events. This page shows 14 solved important MCQs with answers and explanations; all 90 questions on the chapter are available as timed quizzes once you sign in.
Is there an online quiz for Probability?+
Yes — Class 11 Mathematics Probability has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.