Class 9 Maths Ganita Manjari Chapter 7 MCQs – The Mathematics of Maybe: Introduction to Probability – for session 2026-27 exam. If a coin shows heads six times in a row, must the next toss give tails? Learning probability helps you explain why the answer is no. These Class 9 Maths Ganita Manjari Chapter 7 MCQs explore the Maths of Maybe with Probability through familiar situations involving coins, dice, cards and surveys. Work through questions on experimental and theoretical probability, sample spaces, events and tree diagrams. Try each question yourself, then read the explanation to check both your answer and your reasoning.
Class 9 Maths Ganita Manjari Chapter 7 MCQs Set 1
Q1. Which statement best describes a random experiment?
[A]. Its possible outcomes are known, but the outcome of a particular trial cannot be predicted with certainty.
[B]. None of its possible outcomes can be listed.
[C]. Its outcome is always the same.
[D]. It must give every possible outcome in equal numbers of trials.
Q2. Which of the following numbers can represent the probability of an event?
[A]. 5/4
[B]. −0.2
[C]. 0.65
[D]. 1.25
Q3. A standard six-sided die, numbered 1 to 6, is rolled once. What are the probabilities of getting 8 and getting a number less than 7, respectively?
[A]. 1/6 and 5/6
[B]. 0 and 5/6
[C]. 0 and 1
[D]. 1 and 0
Q4. An event has probability 0.75. Which statement correctly describes its chance of occurring?
[A]. It has a 75% chance and is more likely to occur than not occur.
[B]. It has a 7.5% chance of occurring.
[C]. It is certain to occur.
[D]. It is equally likely to occur or not occur.
Q5. When can we calculate an event’s probability by dividing the number of favourable outcomes by the total number of possible outcomes?
[A]. Only after repeating the experiment exactly 100 times.
[B]. Only when the event is certain.
[C]. When all the outcomes being counted are equally likely.
[D]. Whenever the experiment has only two possible outcomes.
Class 9 Maths Ganita Manjari Chapter 7 MCQs Set 2
Q6. For a die roll, S = {1, 2, 3, 4, 5, 6}. Which set represents the event “getting a number greater than 4”?
[A]. {6}
[B]. {4, 5, 6}
[C]. {1, 2, 3}
[D]. {5, 6}
Q7. A coin is tossed twice and the results are recorded in order. Which is the complete sample space? Use H for heads and T for tails.
[A]. {HH, TT}
[B]. {HH, HT, TT}
[C]. {HH, HT, TH, TT}
[D]. {H, T}
Q8. Three coins are tossed, and only the number of heads is recorded. Which is the sample space for the recorded number?
[A]. {1, 2, 3}
[B]. {0, 1, 2}
[C]. {0, 1, 2, 3, 4}
[D]. {0, 1, 2, 3}
Q9. A fair six-sided die is rolled once. What is the probability of getting an even number?
[A]. 1/3
[B]. 2/3
[C]. 1/6
[D]. 1/2
Q10. The 11 letters of PROBABILITY are written separately on 11 identical slips, one letter per slip. One slip is selected at random. What is the probability of selecting B?
[A]. 1/11
[B]. 1/2
[C]. 2/9
[D]. 2/11
Class 9 Maths Ganita Manjari Chapter 7 MCQs Set 3
Q11. A bag contains 3 red balls, 2 blue balls and 1 green ball. Every ball is equally likely to be selected. What is the probability that one randomly selected ball is not red?
[A]. 1/6
[B]. 1/2
[C]. 2/3
[D]. 1/3
Q12. A coin is tossed 50 times and shows heads 28 times. What is the experimental probability of getting tails?
[A]. 11/14
[B]. 11/25
[C]. 14/25
[D]. 1/2
Q13. A paper cup is tossed 100 times. It lands on its bottom 18 times, on its top 12 times and on its side 70 times. What is the experimental probability of landing on its side?
[A]. 7/10
[B]. 7/3
[C]. 1/3
[D]. 3/10
Q14. A representative sample of 40 students includes 9 who prefer the Sports Club. Using this sample, approximately how many students in a school of 800 would be expected to prefer the Sports Club?
[A]. 360
[B]. 180
[C]. 200
[D]. 90
Q15. Which survey method would best help estimate the favourite fruits of students across a whole school?
[A]. Ask only members of one friendship group.
[B]. Ask one student and apply that answer to everyone.
[C]. Randomly select students from different classes and grades.
[D]. Ask only students who already prefer mangoes.
Class 9 Maths Ganita Manjari Chapter 7 MCQs Set 4
Q16. A fair die is rolled many times. What generally happens to the experimental probability of getting 4 as the number of trials becomes very large?
[A]. It must equal 1/6 after every six rolls.
[B]. It tends to get closer to 1/6.
[C]. It becomes 0 because other numbers also occur.
[D]. It steadily increases towards 1.
Q17. A fair coin has shown heads on six consecutive tosses. What is the probability of tails on the next independent toss?
[A]. 0
[B]. 1
[C]. 6/7
[D]. 1/2
Q18. A coin is tossed and a six-sided die is rolled. Both results are recorded. How many outcomes are in the sample space?
[A]. 8
[B]. 12
[C]. 2
[D]. 6
Q19. A student has 2 shirts and 3 pairs of trousers, all different. A tree diagram lists outfits consisting of one shirt and one pair of trousers. How many complete paths will it have?
[A]. 6
[B]. 9
[C]. 5
[D]. 3
Q20. Two fair coins are tossed independently. What is the probability of getting at least one head?
[A]. 1/2
[B]. 1/4
[C]. 1
[D]. 3/4
Class 9 Maths Ganita Manjari Chapter 7 MCQs Set 5
Q21. Three fair coins are tossed independently. What is the probability of getting exactly two heads?
[A]. 1/2
[B]. 3/8
[C]. 7/8
[D]. 1/4
Q22. Three fair coins labelled 1, 2 and 3 are tossed independently. What is the probability that coin 1 shows heads and exactly two heads occur altogether?
[A]. 1/8
[B]. 3/8
[C]. 1/4
[D]. 1/2
Q23. A fair spinner has eight equally likely outcomes numbered 1 to 8. What is the probability that it stops at a multiple of 3?
[A]. 1/8
[B]. 3/8
[C]. 1/2
[D]. 1/4
Q24. Basket A contains one apple and two oranges. Basket B contains one banana and one mango. One fruit is selected independently from each basket, with every individual fruit equally likely within its basket. What is the probability of selecting an apple and a banana?
[A]. 1/6
[B]. 1/2
[C]. 1/4
[D]. 1/3
Q25. A box contains 3 red, 4 black and 2 green pens. Two pens are selected at random, one after another. The first pen is replaced and the pens are mixed before the second selection. What is the probability that both selections have the same colour?
[A]. 29/81
[B]. 52/81
[C]. 1/3
[D]. 29/72
Class 9 Maths Ganita Manjari Chapter 7 MCQs Set 6
Q26. A basket contains 4 red balls and 5 blue balls. Two balls are drawn at random without replacement. What is the probability that the first is red and the second is blue?
[A]. 5/18
[B]. 5/9
[C]. 20/81
[D]. 1/6
Q27. Two fair six-sided dice are rolled independently. What is the probability that their sum is a prime number greater than 5?
[A]. 2/9
[B]. 5/12
[C]. 1/6
[D]. 1/3
Q28. A box contains four balls numbered 1 to 4. Two balls are drawn in order and their numbers are recorded. How many ordered outcomes are possible with replacement and without replacement, respectively?
[A]. 12 and 16
[B]. 16 and 12
[C]. 16 and 16
[D]. 8 and 6
Q29. A student guesses independently on three MCQs. Each question has four options and exactly one correct answer, and each option is equally likely to be chosen. What is the probability of getting exactly two answers correct?
[A]. 27/64
[B]. 3/64
[C]. 9/64
[D]. 1/16
Q30. A circle of diameter 1 m lies completely inside a rectangle measuring 3 m by 2 m. A point is chosen uniformly at random within the rectangle. What is the probability that it lies inside the circle? Give the exact answer in terms of π.
[A]. π/12
[B]. 1/6
[C]. π/24
[D]. π/6
What Are the Key Concepts of Probability in Class 9 Ganita Manjari Chapter 7?
Class 9 Maths Ganita Manjari Part 1 Chapter 7 introduces probability through these core ideas:
- Probability scale: For any event E, 0 ≤ P(E) ≤ 1.
- Special values: An impossible event has probability 0, a certain event has probability 1 and an even-chance event has probability 0.5.
- Experimental probability: Number of times the event occurred ÷ Total number of trials (also called relative frequency).
- Theoretical probability: P(E) = Number of favourable outcomes ÷ Number of possible outcomes, when all outcomes are equally likely.
- Sample space (S): The set of all possible outcomes; the number of outcomes is the sample size, n(S).
- Event: Any subset of the sample space, such as E = {5, 6} for “a number greater than 4” on a die.
- Standard sample spaces: One coin {H, T}; one die {1, 2, 3, 4, 5, 6}; two coins {HH, HT, TH, TT}.
- Tree diagram: A branching diagram that lists every outcome of a multi-step experiment.
- Law of Large Numbers: As trials increase, experimental probability moves closer to theoretical probability.
- Gambler’s Fallacy: Past results do not change the next result; each toss or roll is independent.
Probability Traps That Cost Students Marks
Probability questions look simple, which is exactly why careless slips happen. Keep these points in mind:
- Streak thinking: Six heads in a row does not make tails “due”. A fair coin still gives P(tails) = ½.
- Impossible answers: If your probability is negative or greater than 1, recheck your working.
- Ignoring repeated letters: PROBABILITY has 11 letters and 2 Bs, so P(B) = 2/11, not 1/10.
- Treating HT and TH as the same: With two coins, they are separate outcomes, giving 4 outcomes in total.
- Assuming “two outcomes” means “equally likely”: A car starting or not starting or picking from 3 red and 7 blue marbles, is not a 50-50 situation.
- Mixing up the two types: Use trial data for experimental probability and counting of outcomes for theoretical probability.
- Trusting small samples too much: 3 threes in 12 rolls gives ¼, but the true value for a fair die is ⅙.
- Overlooking “without replacement”: When a ball is not put back, the total in the second draw goes down by one.
- Misreading “at least one”: For two coins, “at least one head” includes HH, HT and TH.
Why Probability Matters Beyond the Exam Hall
Unlike chapters built around fixed formulas and exact answers, Chapter 7 deals with uncertainty and that makes it one of the most useful topics you will study this year. Weather forecasts, cricket tosses, insurance, opinion polls and even board games like Snakes and Ladders, which grew out of India’s ancient Jñān-Chaupad, all depend on the ideas in this chapter. Working through these MCQs helps you think clearly about chance: telling a fair situation from a biased one, choosing between experimental and theoretical methods and resisting the pull of the Gambler’s Fallacy. These are reasoning skills that stay useful long after Class 9.
A Simple Plan to Master Chapter 7
Start with small sets of 10 questions rather than attempting everything at once, and note down each question you miss along with the concept behind it. Probability improves with hands-on practice, so try the chapter’s own activities too: toss a coin 20 times, roll a die, or toss a paper cup and compare your results with the theoretical values. Drawing a quick tree diagram or writing out the sample space before answering will prevent most counting errors. When you get stuck on a textbook question from Exercise Sets 7.1 to 7.4 or the End-of-Chapter Exercises, our NCERT Solutions for Class 9 Maths Ganita Manjari Part 1 Chapter 7 explain every answer step by step.
