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Class 9 Ganita ManjariClass 9 Maths Solutions | 2026–27
Chapter 7: The Mathematics of Maybe: Introduction to ProbabilityPage 167 – 168All 3 Questions on This Page

Class 9 Maths Chapter 7 Exercise Set 7.3 Solutions

Complete step-by-step solutions for Class 9 Mathematics Ganita Manjari Chapter 7 Exercise Set 7.3: Elements of Probability: Sample Spaces and Events (Page 167–168). Covers finding sample spaces, listing outcomes of experiments, and identifying events.

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Key Concepts for Exercise Set 7.3

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1

Sample Space

The sample space, denoted by S, is the set of all possible outcomes of a random experiment.

S = set of all possible outcomes
2

Outcome

An outcome is a possible result of a random experiment.

3

Sample Size

The number of elements in a sample space is called the sample size and is denoted by n(S).

Sample size = n(S)
4

Event

An event is a single possible outcome or a combination of outcomes from a random experiment. An event is a subset of the sample space.

Question 1
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When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space?

Solution

When a 6-sided die is rolled, the possible outcomes are:

1, 2, 3, 4, 5, 6
Thus, the sample space is:

S = {1, 2, 3, 4, 5, 6}

There are 6 possible outcomes.

Therefore,
6

possible outcomes are there in the sample space.

Answer:6 possible outcomes (S = {1, 2, 3, 4, 5, 6})
Question 2
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For the following experiments write down the sample space S. (i) Rolling a die and tossing a coin together. (ii) Choosing a random integer between − 5 and + 5. (iii) A box containing 5 green and 7 red balls. One ball is drawn at random.

Solution
(i) Rolling a die and tossing a coin together:

A die has possible outcomes:

1, 2, 3, 4, 5, 6

A coin has possible outcomes:

H, T

Since both experiments are performed together, each die outcome can occur with either H or T.

Therefore, the sample space is:

S = {(1,H), (1,T), (2,H), (2,T), (3,H), (3,T), (4,H), (4,T), (5,H), (5,T), (6,H), (6,T)}

Hence,

there are 12 possible outcomes.

(ii) Choosing a random integer between −5 and +5:

The integers between −5 and +5, excluding both endpoints, are:

−4, −3, −2, −1, 0, 1, 2, 3, 4

Therefore, the sample space is:

S = {−4, −3, −2, −1, 0, 1, 2, 3, 4}

There are 9 possible outcomes.

Note
When talking about “between” two numbers, we do not include the end numbers. Therefore, between −5 and +5 means: −4 to +4
(iii) A box containing 5 green and 7 red balls. One ball is drawn at random:

The possible colours of the ball drawn are:

Green, Red
Therefore, the sample space is:
S = {Green, Red}
Note
The numbers 5 green and 7 red determine the composition of the box, but the sample space contains the possible outcomes of the experiment, namely Green and Red.
Answer:(i) S = {(1,H), (1,T), (2,H), (2,T), (3,H), (3,T), (4,H), (4,T), (5,H), (5,T), (6,H), (6,T)} | (ii) S = {−4, −3, −2, −1, 0, 1, 2, 3, 4} | (iii) S = {Green, Red}
Question 3
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In a village fair, there are 3 popular snacks available: Samosa, Pakora, and Bhaji. For drinks, villagers can choose either Chai or Lassi. (i) List the sample space of all possible snack and drink combinations a person could choose at the fair. (ii) List the event ‘Selecting Samosa as a snack.’

Solution
(i) List the sample space of all possible snack and drink combinations:

The available snacks are:

Samosa, Pakora, Bhaji

The available drinks are:

Chai, Lassi

Each snack can be combined with either drink.

Therefore, the sample space is:

S = {(Samosa, Chai), (Samosa, Lassi), (Pakora, Chai), (Pakora, Lassi), (Bhaji, Chai), (Bhaji, Lassi)}

Thus, there are 6 possible snack and drink combinations.
(ii) List the event ‘Selecting Samosa as a snack.’:

From the sample space, the combinations in which Samosa is selected are:

E = {(Samosa, Chai), (Samosa, Lassi)}

These are the possible outcomes of the event "Selecting Samosa as a snack."

Answer:(i) S = {(Samosa, Chai), (Samosa, Lassi), (Pakora, Chai), (Pakora, Lassi), (Bhaji, Chai), (Bhaji, Lassi)} (6 combinations) | (ii) E = {(Samosa, Chai), (Samosa, Lassi)}

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