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Mathematics - Probability

Practise 10 IAT (IISER) previous year questions on Probability, compiled from papers spanning 2017 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 IAT (IISER) tests.

Probability has been asked in 9 of the 9 years of IAT (IISER) papers analysed (2017–2026), with 10 questions in all. 10% of them were easy, 90% moderate and 0% tough. Most of its questions came from 2026, with 1 question that year. In the last three years (2023–2026) it had 3 questions across 3 papers, about 1 per paper.

The chapter's 3 topics are not weighted equally: Classical Definition of Probability (5 questions, 50%), Conditional Probability and Multiplication Theorem (4 questions, 40%), and Independent Events (1 question, 10%) have been asked the most. Over the last five years the most frequent topics have been Conditional Probability and Multiplication Theorem (3), Classical Definition of Probability (1), and Independent Events (1).

  1. 1Suppose there are two boxes and , each having 3 red and 4 black balls. One ball is drawn at random from . If it is red, 4 red balls are put 2026Conditional Probability and Multiplication Theorem
  2. 2Five fair coins are tossed independently. What is the probability that at least two heads appear?2025Classical Definition of Probability
  3. 3A ship sets off on a voyage with three engines, labelled A, B, and C, which work independently. The ship can complete the voyage only if at 2024Independent Events
  4. 4Consider three biased coins. Let the probability of getting head be and the probability of getting tail be in each of the coins. Consider th2023Conditional Probability and Multiplication Theorem
  5. 5A randomly chosen card from a deck of 52 cards is given to be a black card (i.e. Spade or Club). What is the probability that it is either a2022Conditional Probability and Multiplication Theorem
  6. 6Out of a pack of ten cards numbered 1 to 10, a boy draws a card at random and keeps it back. Then a girl draws a card at random from the sam2021Conditional Probability and Multiplication Theorem
  7. 7A bag contains 8 balls, of which 5 are green and 3 are red. The probability that two balls chosen at random are of the same colour is:2020Classical Definition of Probability
  8. 8What is the probability that 3 randomly chosen elements from the set satisfy ?2019Classical Definition of Probability
  9. 9A number is picked uniformly randomly from the set of five digit natural numbers. What is the probability that at least one of the digits of2018Classical Definition of Probability
  10. 10Let be a set with 3 elements. What is the probability of choosing an ordered pair of subsets of such that and are disjoint?2017Classical Definition of Probability

Frequently Asked Questions

1.How many questions are available for Probability?

This chapter includes 10 questions compiled from IAT (IISER) papers spanning 2017 to 2026.

2.Are these questions only from IAT (IISER), or from other exams too?

These are IAT (IISER) 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 IAT (IISER) Mathematics?

Probability has appeared in 10 of the 10 years of IAT (IISER) papers covered here, with 10 questions across 10 papers - about one per paper it appears in.

4.What is the difficulty level of Probability questions in IAT (IISER)?

Of the 10 questions analysed for this chapter, 10% are easy, 90% moderate and 0% tough. 2026 had the most, with 1 question.

5.Which topics in Probability should I focus on?

These topics have carried the most weightage in Probability:

  • Classical Definition of Probability - 5 questions (50%)
  • Conditional Probability and Multiplication Theorem - 4 questions (40%)
  • Independent Events - 1 question (10%)
6.Is Probability's weightage in IAT (IISER) going up or down?

Across all 10 papers analysed, Probability has averaged about 1.0 questions per paper. In the last three years (2023–2026), that average has stayed about the same, at about 1.0 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.