CBSE Class 10 Mathematics (Standard) Chapter 14 Probability Important Questions 2027
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21 questions from Probability appeared in 6 of the 7 CBSE papers we analysed (2022–2026) — here are the topics that matter, the questions that repeat, and every previous-year question from this chapter.
Key facts
- Statistics & Probability unit — 11 marks in the official syllabus
- Asked in 6 of 7 analysed papers (2022–2026)
- About 3.0 questions per paper (OR alternatives counted separately)
- 5 question patterns repeated across papers
Important topics in Probability
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Classical probability - numbered tickets/balls/miscellaneous | Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| 2 | Classical probability - dice and coins | Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| 3 | Classical probability - playing cards | Board 2024Board 2025Sample 2025 | ★☆☆☆☆ |
Repeated questions from Probability
1. Two dice: sum/difference event
4×Board 2024Board 2025Board 2026Sample 20261/3 marks
Two dice are thrown at the same time. Determine the probability that the (i) sum of the numbers on the two dice is 5, and (ii) difference of the numbers on the two dice is 3.
2. Draw from a group: favourable/total
3×Board 2023Sample 20251/2 marks
In a bag containing 24 balls, 4 are blue, 11 are green and the rest are white. One ball is drawn at random. The probability that drawn ball is white in colour is A) 1/6 B) 3/8 C) 11/24 D) 5/8
3. Red face card from full deck
2×Board 2025Sample 20251 marks
A card is selected at random from a deck of 52 playing cards. The probability of it being a red face card is : (A) 3/13 (B) 2/13 (C) 1/2 (D) 3/26
4. Number with a property from 1..N
2×Board 2024Board 20261 marks
The probability for a randomly selected number out of 1, 2, 3, 4, ..., 25 to be a composite number is : (A) 15/25 (B) 10/25 (C) 11/25 (D) 9/25
5. Complement rule p + q = 1
2×Board 2023Board 20241 marks
If the probability of a player winning a game is 0.79, then the probability of his losing the same game is: (a) 1.79 (b) 0.31 (c) 0.21% (d) 0.21
Probability questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 0 | 0 |
| Board 2023 | 4 | 5 |
| Board 2024 | 5 | 6 |
| Board 2025 | 3 | 5 |
| Sample 2025 | 4 | 6 |
| Board 2026 | 2 | 4 |
| Sample 2026 | 3 | 5 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Probability
Board 2026 2 questions
The probability for a randomly selected number out of 1, 2, 3, 4, ..., 25 to be a composite number is : (A) 15/25 (B) 10/25 (C) 11/25 (D) 9/25
Two dice are thrown at the same time. Determine the probability that the (i) sum of the numbers on the two dice is 5, and (ii) difference of the numbers on the two dice is 3.
Sample 2026 3 questions
A pair of dice is tossed. The probability of not getting the sum eight is (A) 5/36 (B) 31/36 (C) 5/18 (D) 5/9
If the probability of the letter chosen at random from the letters of the word "Mathematics" to be a vowel is 2/(2x+1), then x is equal to (A) 4/11 (B) 9/4 (C) 11/4 (D) 4/9
On a particular day, Vidhi and Unnati couldn't decide on who would get to drive the car. They had one coin each and flipped their coin exactly three times. The following was agreed upon: 1. If Vidhi gets two heads in a row, she would drive the car. 2. If Unnati gets a head immediately followed by a tail, she would drive the car. Who has greater probability to drive the car that day? Justify your answer.
Board 2025 3 questions
A card is selected at random from a deck of 52 playing cards. The probability of it being a red face card is : (A) 3/13 (B) 2/13 (C) 1/2 (D) 3/26
Assertion (A) : The probability of selecting a number at random from the numbers 1 to 20 is 1. Reason (R) : For any event E, if P(E) = 1, then E is called a sure event. Choose the correct option: (A) Both A and R true, R correct explanation of A (B) Both A and R true, R not correct explanation of A (C) A true, R false (D) A false, R true
Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2.
Sample 2025 4 questions
In a bag containing 24 balls, 4 are blue, 11 are green and the rest are white. One ball is drawn at random. The probability that drawn ball is white in colour is A) 1/6 B) 3/8 C) 11/24 D) 5/8
A card is drawn from a well shuffled deck of playing cards. The probability of getting red face card is A) 3/13 B) 1/2 C) 3/52 D) 3/26
Two dice are rolled together bearing numbers 4, 6, 7, 9, 11, 12. Find the probability that the product of numbers obtained is an odd number.
How many positive three digit integers have the hundredths digit 8 and unit's digit 5? Find the probability of selecting one such number out of all three digit numbers.
Board 2024 5 questions
If the probability of a player winning a game is 0.79, then the probability of his losing the same game is: (a) 1.79 (b) 0.31 (c) 0.21% (d) 0.21
From the data 1, 4, 7, 9, 16, 21, 25, if all the even numbers are removed, then the probability of getting at random a prime number from the remaining is: (a) 2/5 (b) 1/5 (c) 1/7 (d) 2/7
Two dice are rolled together. The probability of getting sum of numbers on the two dice as 2, 3 or 5, is: (a) 7/36 (b) 11/36 (c) 5/36 (d) 4/9
[case context: BINGO game with 75 numbered balls; grouped frequency table of 48 announced numbers in classes 0-15(8), 15-30(9), 30-45(10), 45-60(12), 60-75(9).] When first ball was picked up, what was the probability of calling out an even number?
In a pack of 52 playing cards one card is lost. From the remaining cards, a card is drawn at random. Find the probability that the drawn card is queen of heart, if the lost card is a black card.
Board 2023 4 questions
Probability of happening of an event is denoted by p and probability of non-happening of the event is denoted by q. Relation between p and q is (A) p + q = 1 (B) p = 1, q = 1 (C) p = q - 1 (D) p + q + 1 = 0
A girl calculates that the probability of her winning the first prize in a lottery is 0.08. If 6000 tickets are sold, how many tickets has she bought? (A) 40 (B) 240 (C) 480 (D) 750
In a group of 20 people, 5 can't swim. If one person is selected at random, then the probability that he/she can swim, is (A) 3/4 (B) 1/3 (C) 1 (D) 1/4
A bag contains 4 red, 3 blue and 2 yellow balls. One ball is drawn at random from the bag. Find the probability that drawn ball is (i) red (ii) yellow.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Standard) Chapter 14 Probability?
By how often and how recently they were asked: Classical probability - numbered tickets/balls/miscellaneous; Classical probability - dice and coins; Classical probability - playing cards.
How many marks does Probability carry in the CBSE Class 10 Mathematics (Standard) exam?
Probability is part of the Statistics & Probability unit, which carries 11 marks in the official syllabus. In the analysed papers it had about 3.0 questions per paper.
Do questions from Probability repeat in board exams?
Yes — 5 question patterns from this chapter appeared in two or more past board or official sample papers. They are listed on this page with the years they were asked.