Probability — Class 10 MCQs with Answers
Class 10 CBSE Mathematics · Chapter 14
108 practice questions · 31 Easy · 39 Medium · 38 Hard · Updated
Jump to the 6 solved questions
Practise the most important Class 10 CBSE Mathematics questions from Chapter 14, "Probability". You get 11 timed quizzes made from 108 NCERT-based MCQs, with answers and explanations. The questions are split into 31 Easy, 39 Medium and 38 Hard. Warm up on the basics, then move on to the exam-level questions that top scorers in CBSE Board exams and the JEE & NEET foundation years get right.
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 helps you stay accurate when time is short, just 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 10 Mathematics mastery score. Try the 6 sample questions below: tap an option to see the answer and a worked explanation. Sign in free to start practising.
Probability — important questions & MCQs with answers (Class 10 Mathematics)
6 solved questions from this chapter's difficulty levels, each with its answer and explanation. Tap an option to check yourself.
0 of 6 answered
- Q1 of 6Easy
Probability of any event lies between:
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Answer: 0 and 1
Explanation: By the probability axiom, 0 ≤ P(E) ≤ 1 always — 0 means impossible, 1 means certain; values can never be negative or exceed 1.
- Q2 of 6Easy
When a fair coin is tossed once, P(getting a head) =
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Answer: 1/2
Explanation: Sample space = {H, T}, so 2 equally likely outcomes with 1 favourable (head): P = favourable/total = 1/2.
- Q3 of 6Medium
Two coins are tossed. Probability of getting at least one head:
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Answer: 3/4
Explanation: Total outcomes = 4 (HH, HT, TH, TT). Complement 'no head' is TT only, so P(TT) = 1/4. P(at least one head) = 1 − 1/4 = 3/4. Common mistake: forgetting HT and TH both count.
- Q4 of 6Medium
Assertion (A): When a die is thrown once, the probability of getting a number greater than 4 is 1/3. Reason (R): The sum of the probabilities of all the elementary events of an experiment is 1.
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Answer: Both A and R are true but R is not the correct explanation of A
Explanation: Both are true. A holds because 2 of the 6 outcomes (5 and 6) are greater than 4, so the probability is 2/6 = 1/3. R is a true general fact but is not how A is found, so it does not explain A.
- Q5 of 6Hard
Two dice are thrown together. Probability that the product of the two numbers is greater than 16:
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Answer: 5/18
Explanation: Listing pairs with product over 16 — (3,6),(4,5),(4,6),(5,4),(5,5),(5,6),(6,3),(6,4),(6,5),(6,6) — gives 10 of 36 outcomes: P = 10/36 = 5/18.
- Q6 of 6Hard
Assertion (A): One card is drawn from a well-shuffled deck of 52 cards. The probability that it is a red face card is 3/26. Reason (R): A deck of 52 cards has 4 aces.
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Answer: Both A and R are true but R is not the correct explanation of A
Explanation: Both are true. There are 2 red suits with 3 face cards (king, queen, jack) each, so 6 red face cards and the probability is 6/52 = 3/26. R is a true fact about aces, which are not face cards, so it does not explain A.
Probability notes: key concepts (Class 10 Mathematics)
Probability measures how likely an event is on a scale from 0 to 1. This chapter works with the classical definition based on equally likely outcomes, applying it to the standard experiments boards use — tossing coins, throwing dice, drawing cards and picking balls from a bag.
- Random experiment
- An action whose result cannot be predicted in advance although all possible results are known, such as tossing a coin.
- Outcome
- A single possible result of an experiment — one face of a die, one card from a pack.
- Sample space
- The set of all possible outcomes. Listing it correctly supplies the denominator of every probability.
- Event
- A collection of outcomes of interest, such as 'an even number' when throwing a die.
- Equally likely outcomes
- Outcomes with the same chance of occurring, as with a fair coin or unbiased die. The classical formula requires this.
- Classical (theoretical) probability
- The number of outcomes favourable to the event divided by the total number of equally likely outcomes.
- Range of probability
- Every probability lies between 0 and 1 inclusive; a value outside this range means the counting has gone wrong.
- Sure and impossible events
- An event certain to happen has probability 1; one that cannot happen has probability 0.
- Complementary events
- The event 'not E' together with E covers everything, so P(E) + P(not E) = 1.
- Tossing coins
- One coin gives 2 outcomes, two coins 4 (HH, HT, TH, TT) and three coins 8 — HT and TH are distinct outcomes.
- Throwing dice
- One die gives 6 outcomes and two dice give 36 ordered pairs, the basis for sum, doublet and difference questions.
- Playing cards
- A standard pack has 52 cards: 4 suits of 13, 26 red and 26 black, 12 face cards (J, Q, K) and 4 aces.
- Drawing balls from a bag
- Counting favourable and total balls by colour; the total changes if a ball is not replaced.
- Arrangements of letters
- Selecting a letter at random from a word, where repeated letters increase the favourable count.
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Probability — FAQs
What are the key concepts in Class 10 Mathematics Probability?+
Probability measures how likely an event is on a scale from 0 to 1. This chapter works with the classical definition based on equally likely outcomes, applying it to the standard experiments boards use — tossing coins, throwing dice, drawing cards and picking balls from a bag. Key ideas include Random experiment, Outcome, Sample space, Event, Equally likely outcomes, Classical (theoretical) probability.
What does Class 10 Mathematics Chapter 14 (Probability) cover on XamBaaz?+
It has 108 NCERT-based MCQs on "Probability": 31 Easy, 39 Medium and 38 Hard. Together they make 11 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE Board exams and the JEE & NEET foundation years.
Are these "Probability" questions free to practise?+
Yes. Sign in with Google to practise "Probability" free. Full unlimited access is ₹999/year. One year from the day you pay. You stay in Class 10 till 31 March; on 1 April your account moves up to Class 11 and the rest of your year carries over. 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 11 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. 6 sample questions are on this page with answers: tap an option, or "Show answer", to see the correct option and a step-by-step 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. 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 10 Mathematics)?+
The questions that matter most test Random experiment, Outcome, Sample space, Event, Equally likely outcomes, Classical (theoretical) probability. This page shows 6 solved important MCQs with answers and explanations. Sign in to practise all 108 questions on the chapter as timed quizzes.
Is there an online quiz for Probability?+
Yes — Class 10 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.
Are there question answers and extra questions for Probability (Class 10 Mathematics)?+
Yes. This page has 6 solved questions on Probability, each with the correct answer and a short explanation. Sign in to practise all 108 questions on the chapter as timed quizzes.
Are there assertion–reason and case study questions for Probability (Class 10 Mathematics)?+
Yes. The Probability question bank has 6 assertion–reason questions and 12 case-based (case study) questions in the CBSE board format, alongside the regular MCQs. Each comes with the answer and a worked explanation. Sign in to practise them in timed quizzes.