CBSE Class 9 Maths Chapter 7: The Mathematics of Maybe: Introduction to Probability — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 7: The Mathematics of Maybe: Introduction to Probability from the NCERT Class 9 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Assertion & Reason Questions
1
Assertion (A): Probability measures how likely an event is to occur.
Reason (R): It assigns a numerical measure of likelihood to uncertain outcomes.
Reason (R): It assigns a numerical measure of likelihood to uncertain outcomes.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The numerical scale allows likelihoods to be compared objectively.
2
Assertion (A): In a random experiment, possible outcomes may be known even though the actual outcome of one trial is uncertain.
Reason (R): A subjective probability may be based on a person's interpretation of available evidence.
Reason (R): A subjective probability may be based on a person's interpretation of available evidence.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are true, but subjective judgement does not explain the defining unpredictability of a random experiment.
3
Assertion (A): The outcomes heads and tails are equally likely when a fair coin is tossed.
Reason (R): Knowing this allows the result of the next individual toss to be predicted with certainty.
Reason (R): Knowing this allows the result of the next individual toss to be predicted with certainty.
Answer: (c)
A is true, but R is false. Equal likelihood determines probabilities, not the exact result of a single random trial.
4
Assertion (A): A random experiment must produce exactly the same outcome every time it is repeated.
Reason (R): Repeated random trials can produce different outcomes that cannot be known in advance.
Reason (R): Repeated random trials can produce different outcomes that cannot be known in advance.
Answer: (d)
A is false, but R is true. Variation and uncertainty are central features of random experiments.
5
Assertion (A): The probability of every event lies between 0 and 1 inclusive.
Reason (R): Zero represents impossibility and one represents certainty.
Reason (R): Zero represents impossibility and one represents certainty.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The endpoints and values between them form the probability scale.
6
Assertion (A): An impossible event has probability 0.
Reason (R): A certain event has probability 1.
Reason (R): A certain event has probability 1.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both endpoint facts are correct, but the probability of a certain event does not explain the impossible-event value.
7
Assertion (A): A probability cannot be negative.
Reason (R): A probability may exceed 1 when an event is very likely.
Reason (R): A probability may exceed 1 when an event is very likely.
Answer: (c)
A is true, but R is false. Even a certain event has probability exactly 1, so values above 1 are invalid.
8
Assertion (A): Subjective probability is always computed from long-run relative frequency and is therefore completely objective.
Reason (R): Subjective probability reflects judgement or interpretation of evidence.
Reason (R): Subjective probability reflects judgement or interpretation of evidence.
Answer: (d)
A is false, but R is true. Objective estimates use systematic data or a model, while subjective estimates can vary between people.
9
Assertion (A): Experimental probability equals the number of times an event occurs divided by the total number of trials.
Reason (R): It is based on observed relative frequency in repeated experiments.
Reason (R): It is based on observed relative frequency in repeated experiments.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Counting occurrences and trials produces the empirical estimate.
10
Assertion (A): Experimental probability is obtained from observed trials.
Reason (R): Theoretical probability is obtained from a model of possible outcomes in a fair situation.
Reason (R): Theoretical probability is obtained from a model of possible outcomes in a fair situation.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both descriptions are correct, but the model-based definition does not explain the observed experimental calculation.
11
Assertion (A): Experimental probability often approaches theoretical probability as the number of trials becomes very large.
Reason (R): After only a few trials, the two probabilities must always be exactly equal.
Reason (R): After only a few trials, the two probabilities must always be exactly equal.
Answer: (c)
A is true, but R is false. Small samples can show substantial random variation.
12
Assertion (A): The formula favourable outcomes divided by total outcomes can be used unchanged even when the outcomes are not equally likely.
Reason (R): The simple counting formula assumes all outcomes in the sample space are equally likely.
Reason (R): The simple counting formula assumes all outcomes in the sample space are equally likely.
Answer: (d)
A is false, but R is true. Unequal outcome probabilities require weighting rather than mere counting.
13
Assertion (A): For equally likely outcomes, theoretical probability is the number of favourable outcomes divided by the total number of possible outcomes.
Reason (R): Each outcome contributes the same share of probability in such a model.
Reason (R): Each outcome contributes the same share of probability in such a model.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Equal shares make the probability proportional to the count of favourable outcomes.
14
Assertion (A): Relative frequency from statistical data can estimate probability.
Reason (R): A theoretical probability model may be used when a fair experiment has known equally likely outcomes.
Reason (R): A theoretical probability model may be used when a fair experiment has known equally likely outcomes.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are objective approaches, but the theoretical model does not explain the calculation from observed data.
15
Assertion (A): For two coin tosses, the sample space can be {HH, HT, TH, TT}.
Reason (R): The set {H, T} is a complete sample space for the ordered results of two tosses.
Reason (R): The set {H, T} is a complete sample space for the ordered results of two tosses.
Answer: (c)
A is true, but R is false. The two-toss experiment has four ordered outcomes, not two single-toss outcomes.
16
Assertion (A): An event may contain an outcome that is impossible within the experiment's sample space.
Reason (R): An event is a subset containing one or more outcomes from the sample space, with the empty set representing the impossible event.
Reason (R): An event is a subset containing one or more outcomes from the sample space, with the empty set representing the impossible event.
Answer: (d)
A is false, but R is true. Events must be built from outcomes belonging to the experiment.
17
Assertion (A): A sample space lists all possible outcomes of a random experiment.
Reason (R): An event is formed by selecting one or more outcomes from that sample space.
Reason (R): An event is formed by selecting one or more outcomes from that sample space.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The sample space is the universal set for the events of the experiment.
18
Assertion (A): An event is a subset of the sample space.
Reason (R): A tree diagram can display successive choices and their possible outcomes.
Reason (R): A tree diagram can display successive choices and their possible outcomes.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are correct, but the diagramming method does not explain the set-theoretic definition of an event.
19
Assertion (A): A tree diagram can help calculate probabilities in a multi-stage experiment.
Reason (R): At each branching point, the probabilities of all outgoing branches add to zero.
Reason (R): At each branching point, the probabilities of all outgoing branches add to zero.
Answer: (c)
A is true, but R is false. Outgoing branch probabilities must add to 1.
20
Assertion (A): When objects are drawn without replacement, the probability on later draws always remains unchanged.
Reason (R): Without replacement, the composition of the collection changes and later branch probabilities may change.
Reason (R): Without replacement, the composition of the collection changes and later branch probabilities may change.
Answer: (d)
A is false, but R is true. Removing an object changes both the number and proportions of remaining possibilities.
❓ Frequently Asked Questions
What is covered in CBSE Class 9 Maths Chapter 7 The Mathematics of Maybe: Introduction to Probability?
This chapter covers all key topics from The Mathematics of Maybe: Introduction to Probability as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 9 board exam preparation covering the complete syllabus.
Are these CBSE Class 9 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 9 Maths?
All chapters of CBSE Class 9 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
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