Past papers by chapter · Chapter 13
Probability in past papers.
Every board and sample-paper question on Probability, newest paper first. Each one opens with its full-marks exam answer.
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CBSE Board Examination 2026
CBSE Board Examination 2025
- Board 2025 Q7 for independent events E and F
Independent events and conditional probability1 mark - Board 2025 Q30Absent students: and the mean, or the probability of a distinction
Mean of a distribution; total probability3 marks - Board 2025 Q38Case study: loan defaults at fixed, floating and variable rates
Case study: total probability and Bayes' theorem4 marks
CBSE Board Examination 2024
CBSE Board Examination 2023
CBSE Board Examination 2022 (Term 2)
CBSE Sample Paper 2026-27
- Sample 2026-27 Q16Probability that it rains on three consecutive days
Independent events: multiplication rule1 mark - Sample 2026-27 Q17At least one 4, given the sum on two dice is a multiple of 5
Conditional probability1 mark - Sample 2026-27 Q18Find when exactly one of two independent events has probability
Independent events1 mark - Sample 2026-27 Q35Smartwatch false alerts: total probability and Bayes' theorem
Total probability and Bayes' theorem5 marks
CBSE Sample Paper 2025-26
- Sample 2025-26 Q18Guessing a 6-digit PIN when the first 4 digits are known
Probability: independent choices multiplied1 mark - Sample 2025-26 Q31Mehul and Rashi: chance of Rashi's selection and of at least one
Independent events: exactly one, at least one3 marks - Sample 2025-26 Q38Case study: screen time, anxiety and low retention
Total probability and Bayes' theorem4 marks
CBSE Sample Paper 2024-25
CBSE Sample Paper 2023-24
- Sample 2023-24 Q14Problem solved by at least one of three students (chances )
Independent events: probability of at least one1 mark - Sample 2023-24 Q27Probability distribution : find , and
Random variable: probability distribution3 marks - Sample 2023-24 Q36Case study: error rates of three employees processing forms
Total probability and Bayes' theorem4 marks
CBSE Sample Paper 2022-23
- Sample 2022-23 Q14 for independent events
Independent events and their complements1 mark - Sample 2022-23 Q27Coin tossing for the odd person, or the mean number of defective items
Independent trials; mean of a random variable3 marks - Sample 2022-23 Q38Case study: two antiaircraft guns fire at a plane
Independent events; Bayes' theorem4 marks
CBSE Sample Paper 2021-22 (Term 2)
- Sample 2021-22 T2 Q5Number of red balls in two draws from 1 red and 3 white balls
Probability distribution of a random variable2 marks - Sample 2021-22 T2 Q6Two cards without replacement: first red, second a Jack
Multiplication theorem: without replacement2 marks - Sample 2021-22 T2 Q14Case study: accident-prone policyholders
Total probability and Bayes' theorem4 marks
CBSE Sample Paper 2020-21
- Sample 2020-21 Q15Probability that a problem is solved when A and B try it independently
Independent events: probability of at least one1 mark - Sample 2020-21 Q16Probability that it rains only on the first 4 days of the week
Independent events: rain on given days1 mark - Sample 2020-21 Q18Case study: three employees, their error rates and Bayes' theorem
Total probability and Bayes' theorem4 marks - Sample 2020-21 Q28Distribution of the number of milk chocolates drawn, or
Probability distribution; conditional probability2 marks