Probability — Class 10 MCQs with Answers
Class 10 CBSE Mathematics · Chapter 14
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 10 CBSE Mathematics questions from Chapter 14, "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 Board exams and the JEE & NEET foundation years 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 10 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 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.
Probability — important questions & MCQs with answers (Class 10 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 any event lies between:
A.0 and 100B.−1 and 1C.0 and 1 (inclusive)✓ CorrectD.1 and 10Answer: C. 0 and 1 (inclusive)
Explanation: By the probability axiom, 0 ≤ P(E) ≤ 1 always — 0 means impossible, 1 means certain; values can never be negative or exceed 1.
- Q2Easy
When a fair coin is tossed once, P(getting a head) =
A.1/2✓ CorrectB.1/4C.1D.0Answer: A. 1/2
Explanation: Sample space = {H, T}, so 2 equally likely outcomes with 1 favourable (head): P = favourable/total = 1/2.
- Q3Easy
Probability of an event E is given by:
A.Number of favourable outcomes onlyB.Total outcomesC.(number of favourable outcomes)/(total outcomes)✓ CorrectD.1/total outcomesAnswer: C. (number of favourable outcomes)/(total outcomes)
Explanation: Classical probability is defined as P(E) = (favourable outcomes)/(total equally likely outcomes) — not the favourable count alone.
- Q4Easy
Probability of getting a head when tossing a fair coin:
A.1/4B.1/2✓ CorrectC.1D.0Answer: B. 1/2
Explanation: A coin toss has 2 equally likely outcomes {H, T}; 1 is favourable (head), so P = favourable/total = 1/2.
- Q5Easy
Probability of getting an even number when rolling a fair die:
A.2/3B.1/3C.1/2✓ CorrectD.1/6Answer: C. 1/2
Explanation: Even faces on a die are {2, 4, 6}, 3 out of 6 equally likely outcomes: P = favourable/total = 3/6 = 1/2.
- Q6Easy
A deck of cards has _____ cards in total:
A.52✓ CorrectB.54C.48D.50Answer: A. 52
Explanation: A standard deck has 4 suits × 13 ranks = 52 cards, split evenly into 2 red and 2 black suits.
- Q7Medium
A card is drawn from a standard 52-card deck. P(card is a king) =
A.1/4B.1/26C.1/13✓ CorrectD.1/52Answer: C. 1/13
Explanation: There are 4 kings among 52 cards: P = favourable/total = 4/52 = 1/13 — not 1/4, which is a whole suit's share, not kings alone.
- Q8Medium
Two coins are tossed. Probability of getting at least one head:
A.3/4✓ CorrectB.1/2C.1/4D.1Answer: A. 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.
- Q9Medium
Two dice are rolled. Probability of sum equal to 7:
A.2/9B.1/12C.1/6✓ CorrectD.1/9Answer: C. 1/6
Explanation: Pairs summing to 7 — (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) — give 6 of 36 outcomes: P = 6/36 = 1/6.
- Q10Medium
Probability of drawing a red king from a deck:
A.1/13B.1/26✓ CorrectC.1/52D.2/52Answer: B. 1/26
Explanation: Total cards = 52. Favourable outcomes are red kings only: king of hearts and king of diamonds = 2. P = 2/52 = 1/26. Common mistake: counting all 4 kings instead of just the 2 red ones.
- Q11Medium
From a bag of 5 red, 4 blue, 3 green, probability of NOT red:
A.5/12B.7/12✓ CorrectC.4/12D.8/12Answer: B. 7/12
Explanation: By the complement rule, P(not red) = 1 − P(red) = 1 − 5/12 = 7/12, matching blue + green = 4 + 3 = 7 out of 12.
- Q12Hard
Two dice are rolled. The probability that the sum is 7 is:
A.5/36B.1/6✓ CorrectC.1/9D.7/36Answer: B. 1/6
Explanation: Total outcomes = 6×6 = 36. Favourable pairs summing to 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6. P = favourable/total = 6/36 = 1/6.
- Q13Hard
Three coins are tossed. Probability of at least 2 heads:
A.3/8B.1/2✓ CorrectC.4/8D.2/3Answer: B. 1/2
Explanation: Outcomes with 2 or 3 heads: C(3,2) + C(3,3) = 3 + 1 = 4 out of 8 equally likely outcomes: P = 4/8 = 1/2.
- Q14Hard
Two dice are thrown together. Probability that the product of the two numbers is greater than 16:
A.1/9B.1/6C.5/18✓ CorrectD.2/9Answer: C. 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.
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Start this chapter free →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.
What does Class 10 Mathematics Chapter 14 (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 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 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. 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. 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 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.