Ex 7.3 Class 9 Maths Ganita Manjari Solutions | Sid Classes
Welcome to Sid Classes, your trusted destination for comprehensive academic resources! In this detailed study guide, we present complete solutions for the NCERT Class 9 Maths Ganita Manjari Chapter 7 Exercise 7.3. Designed to reflect how top-scoring students write their solutions and reasoning in school examinations, this walkthrough makes sample spaces, compound experiments, and event subsets entirely clear.
🔑 Key Concepts Used in this Exercise:
- Sample Space (\(S\)): The set of all possible outcomes of a random experiment.
- Compound Experiments: Experiments formed by combining two or more simple experiments (e.g., rolling a die and tossing a coin). Their total outcomes can be found using the fundamental counting principle (\(m \times n\)).
- Event: A subset of the sample space representing specific outcomes of interest.
NCERT Class 9 Maths Ganita Manjari Chapter 7 Exercise 7.3 Solutions
Question 1
When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space?
Solution:
When a single 6-sided die is rolled, each face numbered \(1, 2, 3, 4, 5,\) and \(6\) has an equal chance of appearing.
Sample space \(S = \{1, 2, 3, 4, 5, 6\}\).
Answer: The total number of possible outcomes is \(\mathbf{6}\).
Question 2
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 \(6\) outcomes \(\{1, 2, 3, 4, 5, 6\}\) and a coin has \(2\) outcomes \(\{H, T\}\).
\(S = \{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)\}\) (Total \(12\) outcomes).
(ii) Choosing a random integer between \(-5\) and \(+5\):
\(S = \{-4, -3, -2, -1, 0, 1, 2, 3, 4\}\).
(iii) A box containing 5 green and 7 red balls. One ball is drawn at random:
Considering individual distinguishable balls: \(S = \{G_1, G_2, G_3, G_4, G_5, R_1, R_2, R_3, R_4, R_5, R_6, R_7\}\) (Total \(12\) outcomes), or represented by color types \(\{ \text{Green}, \text{Red} \}\).
Question 3
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) Sample space of all possible snack and drink combinations:
\(S = \{(\text{Samosa}, \text{Chai}), (\text{Samosa}, \text{Lassi}), (\text{Pakora}, \text{Chai}), (\text{Pakora}, \text{Lassi}), (\text{Bhaji}, \text{Chai}), (\text{Bhaji}, \text{Lassi})\}\) (Total \(6\) combinations).
(ii) Event ‘Selecting Samosa as a snack’:
Event \(= \{(\text{Samosa}, \text{Chai}), (\text{Samosa}, \text{Lassi})\}\).
Frequently Asked Questions (FAQs)
Q1: What is a sample space in probability?
A: A sample space is the complete set of all possible distinct outcomes of a random experiment, usually denoted by the letter \(S\).
Q2: How do you find the total number of outcomes in a compound experiment?
A: By using the multiplication rule (fundamental counting principle): if one experiment has \(m\) outcomes and another has \(n\) outcomes, their combination has \(m \times n\) outcomes.
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