CBSE Class 10 Mathematics (Basic) Chapter 14 Probability Important Questions 2027
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25 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 3.6 questions per paper (OR alternatives counted separately)
- 3 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 2023Board 2024Board 2025Board 2026Sample 2026 | ★☆☆☆☆ |
| 3 | Classical probability - playing cards | Board 2023Board 2024 | ★☆☆☆☆ |
Repeated questions from Probability
1. Sure event on a die
2×Board 2025Board 20261 marks
In a random experiment of throwing a die, which of the following is a sure event ? (A) Getting a number between 1 and 6 (B) Getting an odd number < 7 (C) Getting an even number < 7 (D) Getting a natural number < 7
2. Defective pens from a lot
2×Board 2025Board 20263 marks
A lot consists of 200 pens of which 180 are good and the rest are defective. A customer will buy a pen if it is not defective. The shopkeeper draws a pen at random and gives it to the customer. What is the probability that the customer will not buy it ? Another lot of 100 pens containing 80 good pens is mixed with the previous lot of 200 pens. The shopkeeper now draws one pen at random from the entire lot and gives it to the customer. What is the probability that the customer will buy the pen ?
3. Draw a card from 52
2×Board 2023Board 20241 marks
A card is drawn from a well shuffled deck of 52 playing cards. The probability that drawn card is a red queen, is : (a) 1/13 (b) 2/13 (c) 1/52 (d) 1/26
Probability questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 0 | 0 |
| Board 2023 | 6 | 8 |
| Board 2024 | 4 | 5 |
| Board 2025 | 2 | 4 |
| Sample 2025 | 5 | 7 |
| Board 2026 | 2 | 4 |
| Sample 2026 | 6 | 8 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Probability
Board 2026 2 questions
In a random experiment of throwing a die, which of the following is a sure event ? (A) Getting a number between 1 and 6 (B) Getting an odd number < 7 (C) Getting an even number < 7 (D) Getting a natural number < 7
A lot consists of 200 pens of which 180 are good and the rest are defective. A customer will buy a pen if it is not defective. The shopkeeper draws a pen at random and gives it to the customer. What is the probability that the customer will not buy it ? Another lot of 100 pens containing 80 good pens is mixed with the previous lot of 200 pens. The shopkeeper now draws one pen at random from the entire lot and gives it to the customer. What is the probability that the customer will buy the pen ?
Sample 2026 6 questions
An event is most unlikely to happen. Its probability is
A) 0.0001
B) 0.001
C) 0.01
D) 0.1
ASSERTION (A): Two coins are tossed simultaneously. Possible outcomes are two heads, one head and one tail, two tails. Hence, the probability of getting two heads is 1/3.
REASON (R): Probabilities of 'equally likely' outcomes of an experiment are always equal.
A) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
B) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A).
C) Assertion (A) is true but reason (R) is false.
D) Assertion (A) is false but reason (R) is true.
[Blood Donation Centre 2023 distribution of blood/Rhesus types (in %): O^- = x, O^+ = 30, A^- = 8, A^+ = 24, B^- = 6, B^+ = 18, {AB}^- = 1, {AB}^+ = 3.] Find the value of x.
[Blood Donation Centre 2023 distribution of blood/Rhesus types (in %): O^- = x, O^+ = 30, A^- = 8, A^+ = 24, B^- = 6, B^+ = 18, {AB}^- = 1, {AB}^+ = 3.] Find the probability that a randomly selected person has a Rhesus negative blood type.
[Blood Donation Centre 2023 distribution of blood/Rhesus types (in %): O^- = x, O^+ = 30, A^- = 8, A^+ = 24, B^- = 6, B^+ = 18, {AB}^- = 1, {AB}^+ = 3.] What is the probability that the person selected from the record is Rhesus positive but neither blood type A nor B?
[Blood Donation Centre 2023 distribution of blood/Rhesus types (in %): O^- = x, O^+ = 30, A^- = 8, A^+ = 24, B^- = 6, B^+ = 18, {AB}^- = 1, {AB}^+ = 3.] People with blood type AB positive ({AB}^+) are known as the universal recipient and with blood type O negative (O^-) are known as universal donor. Find the probability of a selected person to be neither universal recipient nor universal donor.
Board 2025 2 questions
In a random experiment of throwing a die, which of the following is a sure event ? (A) Getting a number between 1 and 6 (B) Getting an odd number < 7 (C) Getting an even number < 7 (D) Getting a natural number < 7
A lot consists of 200 pens of which 180 are good and the rest are defective. A customer will buy a pen if it is not defective. The shopkeeper draws a pen at random and gives it to the customer. What is the probability that the customer will not buy it ? Another lot of 100 pens containing 80 good pens is mixed with the previous lot of 200 pens. The shopkeeper now draws one pen at random from the entire lot and gives it to the customer. What is the probability that the customer will buy the pen ?
Sample 2025 5 questions
Which of the following cannot be the probability of an event? (A) 0.4 (B) 4% (C) 0.04% (D) 4
[Case study: A survey of 200 students on preferred mode of transport to school — 120 preferred to walk, 25% preferred bicycles, 10% preferred the bus, and the remaining preferred to be dropped off by car.] What is the probability that a randomly selected student does not prefer to walk to school?
[Case study: A survey of 200 students on preferred mode of transport to school — 120 preferred to walk, 25% preferred bicycles, 10% preferred the bus, and the remaining preferred to be dropped off by car.] Find the probability of a randomly selected student who prefers to walk or use a bicycle.
[Case study: A survey of 200 students on preferred mode of transport to school — 120 preferred to walk, 25% preferred bicycles, 10% preferred the bus, and the remaining preferred to be dropped off by car.] One day 50% of walking students decided to come by bicycle. What is the probability that a randomly selected student comes to school using a bicycle on that day?
[Case study: A survey of 200 students on preferred mode of transport to school — 120 preferred to walk, 25% preferred bicycles, 10% preferred the bus, and the remaining preferred to be dropped off by car.] What is the probability that a randomly selected student prefers to be dropped off by car?
Board 2024 4 questions
If probability of winning a game is p, then probability of losing the game is : (a) 1+p (b) -p (c) p-1 (d) 1-p
A card is drawn from a well shuffled deck of 52 playing cards. The probability that drawn card is a red queen, is : (a) 1/13 (b) 2/13 (c) 1/52 (d) 1/26
Two dice are rolled together. The probability of getting a doublet is : (a) 2/36 (b) 1/36 (c) 1/6 (d) 5/6
A bag contains 4 red, 5 white and some yellow balls. If probability of drawing a red ball at random is 1/5, then find the probability of drawing a yellow ball at random.
Board 2023 6 questions
A card is drawn at random from a well-shuffled deck of 52 cards. The probability of getting a red card is : (a) 1/26 (b) 1/13 (c) 1/4 (d) 1/2
A die is thrown once. Find the probability of getting a number less than 7. (a) 5/6 (b) 1 (c) 1/6 (d) 0
[Case: In a sample of 50 people, 21 had type O blood, 22 had type A, 5 had type B and the rest had type AB blood group.] What is the probability that a person chosen at random had type O blood ?
[Case: In a sample of 50 people, 21 had type O blood, 22 had type A, 5 had type B and the rest had type AB blood group.] What is the probability that a person chosen at random had type AB blood group ?
[Case: In a sample of 50 people, 21 had type O blood, 22 had type A, 5 had type B and the rest had type AB blood group.] What is the probability that a person chosen at random had neither type A nor type B blood group ?
[Case: In a sample of 50 people, 21 had type O blood, 22 had type A, 5 had type B and the rest had type AB blood group.] What is the probability that person chosen at random had either type A or type B or type O blood group ?
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Basic) 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 (Basic) exam?
Probability is part of the Statistics & Probability unit, which carries 11 marks in the official syllabus. In the analysed papers it had about 3.6 questions per paper.
Do questions from Probability repeat in board exams?
Yes — 3 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.