CBSE Class 10 Maths Chapter 14 — Probability: NCERT Solutions, Sample Space, Event Types and 25 Practice MCQs 2027

Last Updated: May 2026 | Reading time: 14 minutes | NCERT-aligned for CBSE Board Exam 2027

If you are searching for the most reliable, exam-focused guide on CBSE Class 10 Maths Chapter 14 Probability, you are in the right place. Probability is the very last chapter in the NCERT Class 10 Maths textbook and consistently delivers 5 to 6 guaranteed marks in the CBSE Board Exam 2027 — yet it remains one of the most under-prepared chapters because students push it to the end of their revision cycle. This pillar guide gives you every formula, every NCERT exercise solution outline, the most common question patterns, a full set of 25 practice MCQs aligned with the latest CBSE sample paper, and a quick-revision checklist designed for the final 7 days before your exam.

Why Probability Is a Scoring Chapter for CBSE Class 10 Boards

The empirical probability chapter is mathematically simple — there is essentially one core formula — but the wording of board questions trips many students up. CBSE has consistently asked 1-mark MCQs, 2-mark short-answer questions, and one 3-mark application question (cards, dice, balls in a bag) every single year since 2020. Once you internalise the sample space and a clean tabular approach, this chapter becomes a guaranteed full-mark zone.

Quick Stats from CBSE Past Papers (2020 to 2025)

• Average marks asked: 5.4 marks per paper
• Most repeated context: dice, deck of 52 cards, coloured balls in a bag
• Difficulty level: 1 easy + 1 medium + 0 to 1 HOTS
• Recommended preparation time: 3 to 4 hours total

Probability — Core Concept and Formulas

Class 10 deals only with theoretical probability (also called classical or mathematical probability) — not the empirical version you saw in Class 9. The single master formula you must memorise is:

P(E) = Number of favourable outcomes ÷ Total number of possible outcomes

Formula and Result Table — Memorise This Before the Exam

NCERT Class 10 Maths Chapter 14 Probability — Exercise-wise Solutions Outline

Exercise 14.1 — Foundation Set (25 Questions)

This is the only exercise in the chapter (NCERT 2024 rationalised edition removed Exercise 14.2). Below is the strategic breakdown:

Q1 — Filling Blanks (Conceptual)

Tests knowledge that probability lies between 0 and 1, the sum P(E) + P(not E) = 1, and definitions of sure/impossible events. Tip: Memorise the four blanks word-for-word — CBSE has lifted this directly into a 1-mark MCQ in 2022 and 2024.

Q2 — Equally Likely Outcomes Identification

Students must identify which experiments have equally likely outcomes. The classic trap: a baby being born is NOT equally likely to be a boy/girl in real-world data (slightly more boys), but for exam purposes we treat it as equally likely. Always justify with a one-line reason.

Q3 — Coin Toss Fairness

Tossing a coin to decide who plays first in football is a fair method because P(Head) = P(Tail) = 1/2. State the formula and the conclusion separately for full marks.

Q4 to Q9 — Single Event Probability (Bag, Die, Coin)

Pure substitution into P(E) = favourable / total. Common contexts: marbles in a bag, ball drawn at random, single die roll. Show n(E) and n(S) on separate lines.

Q10 to Q15 — Cards from a Deck

Standard deck questions. Recreate the 52-card matrix in your rough work: 4 suits × 13 ranks. Common asks: P(red king), P(face card), P(spade or queen), P(neither ace nor king).

Q16 to Q20 — Two Dice

Always start with the 6×6 grid showing 36 ordered pairs. Mark favourable outcomes. Common contexts: sum = 7, sum > 9, doubles, product is even.

Q21 to Q25 — Defective Items, Date / Day, Geometric Probability

The pen/bulb defective questions test conditional thinking. Geometric probability (dart on dartboard) was added in the 2024 syllabus update — area-based instead of count-based.

Solved Example — The Most-Asked Two-Dice Question

Question: Two dice are rolled simultaneously. Find the probability that the sum of numbers appearing on the two dice is (i) 8, (ii) more than 10, (iii) less than or equal to 5.

Solution:

• Sample space n(S) = 36 ordered pairs
• (i) Sum = 8: {(2,6),(3,5),(4,4),(5,3),(6,2)} ⇒ n(E) = 5 ⇒ P(E) = 5/36
• (ii) Sum > 10 means 11 or 12: {(5,6),(6,5),(6,6)} ⇒ n(E) = 3 ⇒ P(E) = 3/36 = 1/12
• (iii) Sum ≤ 5: {(1,1)(1,2)(1,3)(1,4)(2,1)(2,2)(2,3)(3,1)(3,2)(4,1)} ⇒ n(E) = 10 ⇒ P(E) = 10/36 = 5/18

HOTS Question Pattern — Word Problems on Probability

Sample HOTS: A box contains 90 discs numbered from 1 to 90. If one disc is drawn at random, find the probability that it bears (i) a two-digit number, (ii) a perfect square, (iii) a number divisible by 5.

Always list the favourable set explicitly. (i) two-digit numbers from 10 to 90 = 81 numbers, P = 81/90 = 9/10. (ii) perfect squares 1, 4, 9, 16, 25, 36, 49, 64, 81 = 9 numbers, P = 9/90 = 1/10. (iii) multiples of 5 from 5 to 90 = 18 numbers, P = 18/90 = 1/5.

25 Practice MCQs for CBSE Class 10 Probability Board Exam 2027

Take 30 minutes to attempt these without a calculator and check your answers below. The pattern matches CBSE Sample Paper 2026-27 difficulty.

1. The probability of an impossible event is: (a) 1 (b) 0 (c) 1/2 (d) cannot be defined
2. If P(A) = 0.6, then P(not A) is: (a) 0.4 (b) 0.6 (c) 0.5 (d) 1.6
3. The maximum value of probability of any event is: (a) 0 (b) 1 (c) 100 (d) infinity
4. A coin is tossed once. Probability of getting a head: (a) 1 (b) 0 (c) 1/2 (d) 1/4
5. Two coins are tossed simultaneously. Probability of getting at least one head: (a) 1/4 (b) 1/2 (c) 3/4 (d) 1
6. A die is thrown once. Probability of getting an even prime number: (a) 1/6 (b) 1/3 (c) 1/2 (d) 0
7. From a deck of 52 cards, probability of drawing a king of red colour: (a) 1/26 (b) 1/13 (c) 2/13 (d) 1/52
8. A bag contains 5 red, 8 blue and 7 green balls. Probability of drawing a blue ball: (a) 5/20 (b) 8/20 (c) 7/20 (d) 2/5
9. Probability of getting a sum of 7 when two dice are rolled: (a) 1/6 (b) 5/36 (c) 7/36 (d) 1/12
10. A card is drawn from a well-shuffled deck. Probability of drawing a face card: (a) 3/13 (b) 1/4 (c) 4/13 (d) 12/52
11. The sum of probabilities of all elementary events of an experiment equals: (a) 0 (b) 1 (c) any value (d) cannot say
12. If a number is selected at random from 1 to 25, probability that it is a prime: (a) 9/25 (b) 8/25 (c) 7/25 (d) 1/5
13. A die is thrown twice. Probability of getting 6 in the first throw and 5 in the second: (a) 1/12 (b) 1/36 (c) 11/36 (d) 1/6
14. From letters of word PROBABILITY, probability of choosing a vowel: (a) 4/11 (b) 3/11 (c) 7/11 (d) 5/11
15. A child has a die whose six faces show A, B, C, D, E, F. Probability of getting a vowel: (a) 1/3 (b) 1/2 (c) 2/3 (d) 5/6
16. One ticket is drawn at random from tickets numbered 1 to 30. Probability that it is a multiple of 3 or 5: (a) 14/30 (b) 7/15 (c) 1/2 (d) 13/30
17. Two dice are thrown together. Probability of getting a doublet: (a) 1/6 (b) 5/36 (c) 1/3 (d) 1/4
18. A card is drawn from 52 cards. Probability that it is neither an ace nor a king: (a) 11/13 (b) 1/13 (c) 12/13 (d) 2/13
19. If two coins are tossed, probability of getting exactly one tail: (a) 1/4 (b) 1/2 (c) 3/4 (d) 0
20. The probability of getting 53 Sundays in a non-leap year: (a) 1/7 (b) 2/7 (c) 53/365 (d) 1/52
21. The probability of getting 53 Mondays in a leap year: (a) 2/7 (b) 1/7 (c) 53/366 (d) 1/52
22. A card is drawn from 52 cards. Probability that it is a black queen: (a) 1/26 (b) 1/13 (c) 1/52 (d) 2/13
23. If P(E) = 0.05, then P(not E) is: (a) 0.05 (b) 0.5 (c) 0.95 (d) 1.05
24. A bag contains 3 red and 2 blue marbles. Probability of NOT drawing a red marble: (a) 3/5 (b) 2/5 (c) 1/5 (d) 1
25. From numbers 1 to 100, probability that a number selected is a perfect square: (a) 1/10 (b) 1/100 (c) 9/100 (d) 1/9

Answer Key

1.b | 2.a | 3.b | 4.c | 5.c | 6.a | 7.a | 8.d | 9.a | 10.a | 11.b | 12.a | 13.b | 14.a | 15.a | 16.b | 17.a | 18.a | 19.b | 20.a | 21.a | 22.a | 23.c | 24.b | 25.a

Common Mistakes Students Make in Probability

1. Forgetting that 1 is NOT a prime number. Many students count 1 as prime in number-selection questions — costs an easy mark.
2. Confusing "at least" with "exactly". "At least one head" = HH + HT + TH; "exactly one head" = HT + TH only.
3. Mis-counting two-dice sum outcomes. Always draw the 6×6 grid first.
4. Forgetting the complement rule. P(not E) = 1 – P(E) often saves you 4 lines of working.
5. Writing decimal answers for fraction questions. CBSE prefers fractions in lowest form unless otherwise asked.

Last-7-Day Revision Plan for Probability Chapter

• Day 1: Re-read the NCERT chapter (only 18 pages) + write the formula table from memory
• Day 2: Solve all Exercise 14.1 questions in one sitting (90 min)
• Day 3: Solve last 5 years CBSE board questions (search by chapter)
• Day 4: Attempt 25 MCQs above + 15 from sample paper
• Day 5: Re-do only the questions you got wrong
• Day 6: Mock test — 1 hour, 20 questions, score yourself honestly
• Day 7: Glance at the formula table only; do not learn anything new

FAQs — CBSE Class 10 Maths Chapter 14 Probability

Q1. How many marks does Probability carry in the CBSE Class 10 Board Exam 2027?

Based on the latest CBSE Class 10 Maths blueprint and Sample Paper 2026-27, Probability carries 5 to 6 marks. This usually breaks down into one 1-mark MCQ, one 2-mark short answer, and one 3-mark long answer or case-based question.

Q2. Is the Probability chapter difficult to score in?

Probability is among the easiest scoring chapters in Class 10 Maths because the entire chapter relies on a single formula. The challenge lies only in carefully counting the sample space and favourable outcomes. With 4 hours of focused practice, almost every student can score full marks.

Q3. Has NCERT Probability syllabus changed for the 2027 board exam?

Yes. In the 2024 NCERT rationalisation, Exercise 14.2 was removed and the chapter is now condensed to a single Exercise 14.1 with 25 questions. Geometric probability based on areas was introduced in the revised edition. Always practice from the latest 2024 NCERT textbook, not older 2020 editions.

Q4. What is the difference between theoretical and experimental probability?

Theoretical probability assumes all outcomes are equally likely and is computed using the ratio formula P(E) = favourable outcomes / total outcomes. Experimental probability is computed from actual trial data — number of times the event occurred divided by the total number of trials. Class 10 deals only with theoretical probability.

Q5. How can I get my Probability answers checked daily before the board exam?

Use the Ready For Boards AI answer checking platform — upload a hand-written solution and receive an evaluation in under 30 seconds with marking-scheme-aligned feedback. This is the only board-exam-focused AI grader in India and helps build the writing speed and presentation discipline that CBSE examiners reward.

Internal Resources to Continue Your Class 10 Preparation

• CBSE Class 10 Maths Chapter 13 — Statistics
• CBSE Class 10 Maths Chapter 12 — Surface Area and Volume
• CBSE Class 10 Maths Chapter 7 — Coordinate Geometry
• CBSE Sample Paper 2027 with Marking Scheme
• CBSE Previous Year Papers — Chapter-wise Analysis

Try the In-Page Quiz

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Bookmark this page and revisit on the day before your board exam — the formula table, two-dice grid and 25-MCQ section are all the revision you will need to lock in your full marks on Probability.