Jump to a section

Mathematics - Probability

Practise 20 NEST (NISER) previous year questions on Probability, compiled from papers spanning 2012 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty NEST (NISER) tests.

Probability has been asked in 13 of the 16 years of NEST (NISER) papers analysed (2011–2026), with 20 questions in all. 5% of them were easy, 80% moderate and 15% tough. Most of its questions came from 2026, with 3 questions that year. In the last three years (2024–2026) it had 7 questions across 4 papers, about 1.8 per paper.

The chapter's 6 topics are not weighted equally: Classical Definition of Probability (6 questions, 30%), Conditional Probability and Multiplication Theorem (6 questions, 30%), and Bernoulli Trial and Binomial Distribution (3 questions, 15%) have been asked the most. Over the last five years the most frequent topics have been Conditional Probability and Multiplication Theorem (4), Classical Definition of Probability (3), and Total Probability (2). Classical Definition of Probability has produced the most tough questions (1).

  1. 1Amar, Akbar, and Anthony write a test independently. The probability that Amar passes the test and Akbar fails the test is . The probability2026Independent Events
  2. 2The probability that the sum of two integers and , where , chosen randomly and independently, being divisible by is2026Classical Definition of Probability
  3. 3In a building, an elevator starts from the ground floor (that is, 0th floor) with passengers and stops at every floor until the 15th floor w2026Classical Definition of Probability
  4. 4Let and be three 3 -digit numbers chosen randomly. Then the probability that is divisible by number 3 is2025Classical Definition of Probability
  5. 5Let and be two students who have appeared NEST. Given that i. the probability that X qualifies NEST is ; ii. the probability that X qualifie2025Conditional Probability and Multiplication Theorem
  6. 6A man has two homes - one in city A and another in city B . He travels between these two cities by flights. The only flight from city A to c2024 (Session 1)Total Probability
  7. 7The sports club in a university changes its president every semester. Last year, the president for the first semester was chosen randomly fr2024 (Session 2)Conditional Probability and Multiplication Theorem
  8. 8In a throw of a (biased single) dice, the probability of the outcome being a number is if is even, and if is odd. If the dice is thrown twic2023 (Session 1)Total Probability
  9. 9If a teacher assigns homework on the th day, the probability that she will assign homework on the th day is . If she does not assign homewor2023 (Session 2)Conditional Probability and Multiplication Theorem
  10. 10Class XI has 4 boys and 6 girls, and Class XII has 4 boys and 3 girls. One student is selected at random from one of the classes (either cla2022 (Session 1)Baye's Theorem
  11. 11The probabilities of getting a head for one coin is and for an another coin is . If both the coins are tossed simultaneously, then the proba2022 (Session 2)Conditional Probability and Multiplication Theorem
  12. 12Let A, B and C be three events with non-zero probabilities. Then2020 (Session 1)Conditional Probability and Multiplication Theorem
  13. 13A six-faced unbiased die is thrown until a number greater than 4 appears. The probability that this occurs on the -th throw, where is an eve2019 (Session 1)Bernoulli Trial and Binomial Distribution
  14. 14A box contains more than 100 balls of which some are red and the remaining are blue. If we take out two balls at random, the probability of 2019 (Session 2)Classical Definition of Probability
  15. 15A bag contains 10 coins numbered . Three friends and play a game. First, picks a coin randomly from the bag, notes down the number and retur2018Classical Definition of Probability
  16. 16An examination consists of 10 multiple choice questions, where each question has 4 options, only one of which is correct. In every question,2017Bernoulli Trial and Binomial Distribution
  17. 17In an office, of the employees have scooters and have cars. Among those who have scooters, do not have cars. The probability that an employe2016Conditional Probability and Multiplication Theorem
  18. 18There are 10 black balls in a box. A person picks 5 balls from the box, paints them white and puts them back into the box. Now the person pi2015Classical Definition of Probability
  19. 19Each of the three children in a family is equally likely to be a boy or a girl independent of the others. Define the events "all the childre2014Independent Events
  20. 20A fair coin is repeatedly tossed. Let be the event that we get at least 2 heads in 4 tosses and be the event that we get at least 3 heads in2012Bernoulli Trial and Binomial Distribution

Frequently Asked Questions

1.How many questions are available for Probability?

This chapter includes 20 questions compiled from NEST (NISER) papers spanning 2012 to 2026.

2.Are these questions only from NEST (NISER), or from other exams too?

These are NEST (NISER) questions specifically for the Probability chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Probability an important chapter for NEST (NISER) Mathematics?

Probability has appeared in 13 of the 16 years of NEST (NISER) papers covered here, with 20 questions across 17 papers - about one per paper it appears in.

4.What is the difficulty level of Probability questions in NEST (NISER)?

Of the 20 questions analysed for this chapter, 5% are easy, 80% moderate and 15% tough. 2026 had the most, with 3 questions.

5.Which topics in Probability should I focus on?

These topics have carried the most weightage in Probability:

  • Classical Definition of Probability - 6 questions (30%)
  • Conditional Probability and Multiplication Theorem - 6 questions (30%)
  • Bernoulli Trial and Binomial Distribution - 3 questions (15%)
  • Classical Definition of Probability has produced the most tough questions (1).
6.Is Probability's weightage in NEST (NISER) going up or down?

Across all 17 papers analysed, Probability has averaged about 1.2 questions per paper. In the last three years (2024–2026), that average has risen, at about 1.8 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.