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Class 10 Maths Chapter 14: Probability — Important Questions & Sample Paper

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Reviewed by qpaper's CBSE curriculum team · Edited by Mohit · Updated June 2026

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Yes — this page has 44+ original Class 10 Mathematics Chapter 14 (“Probability”) important questions with answers (Multiple Choice (MCQ), Assertion–Reason, Short Answer, Short Answer, Long Answer, Case Study). Practise them free, or generate a full CBSE board-pattern sample paper (80 marks) and export it to PDF or Word — in English & Hindi, for 2026-27.

Chapter 14 Probability introduces the fundamental concepts of random experiments, outcomes, and events. Students learn to define sample space and apply the classical definition of probability: P(E) = (Number of favourable outcomes)/(Total number of outcomes). The chapter covers mutually exclusive events, complementary events, and the probability of compound events using simple set operations. Important skills include listing outcomes systematically for experiments like tossing coins and dice, drawing cards from a deck, and selecting balls from bags. CBSE exams typically feature questions on finding probabilities in single-step experiments (like drawing a card or ball) and two-step experiments (like tossing two coins or rolling two dice). Students are also tested on conditions involving sums or products, prime numbers, and complementary probabilities. A common question type involves determining an unknown number of items given a probability. Mastering this chapter builds a strong foundation for higher-level probability in later classes.

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Mathematics — Probability

Class 10Time: 3 hrsMax Marks: 80

SECTION A

  1. 1.

    A fair die is thrown once. What is the probability of getting an even number?

    (a) 1/2(b) 1/3(c) 1/6(d) 2/3
    1
  2. 2.

    One card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is either a king or a black card?

    (a) 1/26(b) 7/13(c) 15/26(d) 8/13
    1
  3. 3.

    Which of the following cannot be the probability of an event?

    (a) 0.75(b) 0.2(c) 1.5(d) 1
    1

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Marks distribution & blueprint

In a CBSE exam, this chapter typically contributes questions across the following types. The last column shows how many original questions of each type we have ready in our bank for this chapter:

Question typeMarks eachIn our bank
Multiple Choice (MCQ)1 mark13
Assertion–Reason1 mark6
Short Answer2 marks8
Short Answer3 marks6
Long Answer5 marks5
Case Study4 marks6

44 original, exam-style questions in our bank for this chapter — with answers.

Important & sample questions (with answers)

Real, exam-style questions to practise and revise — each with its answer. Generate a full paper for unlimited more.

  1. Q1. A fair die is thrown once. What is the probability of getting an even number?

    1 mark
    Multiple Choice (MCQ)
    (A) 1/2(B) 1/3(C) 1/6(D) 2/3
    ▸ Answer

    1/2

  2. Q2. One card is drawn from a well-shuffled deck of 52 cards. What is the probability that it is either a king or a black card?

    1 mark
    Multiple Choice (MCQ)
    (A) 1/26(B) 7/13(C) 15/26(D) 8/13
    ▸ Answer

    7/13

  3. Q3. Which of the following cannot be the probability of an event?

    1 mark
    Multiple Choice (MCQ)
    (A) 0.75(B) 0.2(C) 1.5(D) 1
    ▸ Answer

    1.5

  4. Q4. Two unbiased coins are tossed simultaneously. What is the probability of getting exactly one head?

    1 mark
    Multiple Choice (MCQ)
    (A) 1/4(B) 1/2(C) 3/4(D) 1
    ▸ Answer

    1/2

  5. Q5. Assertion (A): The probability of getting a head when a fair coin is tossed once is 1/2. Reason (R): When a coin is tossed, there are two possible outcomes, head or tail.

    1 mark
    Assertion–Reason
    (A) Both A and R are true and R is the correct explanation of A.(B) Both A and R are true but R is not the correct explanation of A.(C) A is true but R is false.(D) A is false but R is true.
    ▸ Answer

    Both A and R are true and R is the correct explanation of A.

  6. Q6. A box contains 18 balls, of which x are black. When one ball is drawn at random, the probability that it is black is 5/9. Find the value of x.

    2 marks
    Short Answer
    ▸ Answer

    10

  7. Q7. One card is drawn at random from a well‑shuffled deck of 52 playing cards. Find the probability that it is a red card or a king.

    2 marks
    Short Answer
    ▸ Answer

    7/13

  8. Q8. A bag contains 12 balls out of which x are white. If 6 more white balls are put in the bag, the probability of drawing a white ball is double what it was before. Find x.

    3 marks
    Short Answer
    ▸ Answer

    3

  9. Q9. A bag contains 4 white, 3 blue and 5 red balls. Two balls are drawn at random without replacement. Find the probability that at least one of them is red.

    3 marks
    Short Answer
    ▸ Answer

    15/22

  10. Q10. Two dice are thrown simultaneously. Find the probability of getting (i) a sum of 10, (ii) a doublet, (iii) a sum of at least 9.

    5 marks
    Long Answer
    ▸ Answer

    (i) 1/12, (ii) 1/6, (iii) 5/18

  11. Q11. A die is thrown once. Find the probability of getting (i) an even prime number, (ii) a number less than 4, (iii) a number which is a multiple of 2 or 3.

    5 marks
    Long Answer
    ▸ Answer

    (i) 1/6, (ii) 1/2, (iii) 2/3

  12. Q12. In a certain game, a player rolls two fair dice simultaneously: one red die and one blue die. The number on the red die becomes the tens digit, and the number on the blue die becomes the units digit of a two-digit number (for example, a red 3 and a blue 5 form the number 35). Assume all outcomes are equally likely.

    4 marks
    Case Study
    1. (i) Find the probability that the number formed is a prime number.2 marks
    2. (ii) Find the probability that the number formed is divisible by 3.2 marks
    ▸ Answer

    (i) 2/9, (ii) 1/3

Frequently asked questions

What is the basic probability formula taught in this chapter?

The probability of an event E is given by P(E) = (Number of outcomes favourable to E) / (Total number of possible outcomes). This applies only when all outcomes are equally likely.

How do I list outcomes when two coins are tossed?

When two coins are tossed, the sample space = {HH, HT, TH, TT}, where H is heads and T is tails. There are 4 equally likely outcomes. For three coins, it's {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}—8 outcomes.

What is a complementary event and how is its probability found?

A complementary event E′ consists of all outcomes not in event E. Its probability is P(E′) = 1 − P(E). This is often used to find the probability of 'at least one' scenarios by subtracting the probability of 'none' from 1.

What types of questions on dice appear in CBSE exams?

Typical dice questions involve throwing one or two dice. With two dice, total outcomes = 36. You may be asked to find the probability of sums (e.g., prime, even, 8), products (e.g., multiple of 4), or specific doublets. Always list ordered pairs systematically.

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