NCERT Solutions Class 9 Maths Introduction to Probability

The Class 9 academic year is critical to a student’s education. It is a foundation for the Class 10 board exams and sets the tone for future academic pursuits. The National Council of Educational Research and Training (NCERT) provides widely used textbooks across India, and mastering the content in these books is essential for success. To help students tackle the rigorous demands of Class 9 maths studies, NCERT solutions for Class 9 maths serve as a reliable companion.

NCERT solutions for Class 9 Maths – Introduction to Probability provide step-by-step answers to textbook questions, making the subject approachable and engaging.

Please Note: This chapter has been removed from the class 9 syllabus as per the latest revised NCERT syllabus of 2024-25.

1.0NCERT Solutions Class 9 Maths Introduction to Probability: Download Free PDF

2.0NCERT Solutions for Class 9 Maths Introduction to Probability: Points to Remember

Here are the key topics and their definitions covered in Class 9 Probability:

1. What Is Probability?

In simple terms, probability measure of the likelihood that an event will occur. It quantifies uncertainty and provides a mathematical framework to analyze random events. Probability is expressed as a number between 0 and 1:

• 0 indicates that an event is impossible.
• 1 indicates that an event is certain.

2. Experiment: An activity with well-defined outcomes.

Example: Tossing a coin, rolling a dice, drawing a card from a deck.

3. Trial: Each repetition of an experiment.

Example: Tossing a coin twice involves two trials.

4. Outcome: A possible result of a trial.

Example: Heads or tails in a coin toss, a number from 1 to 6 on a dice.

5. Event: A collection of one or more outcomes.

Example: Getting an even number on a dice roll (event: {2, 4, 6}).

6. Experimental Probability (Empirical Probability): The ratio of the number of  an event occurs to the total number of trials.

Formula: P(E) = $\frac{NumberoftimeseventEoccurs}{Totalnumberoftrials}$

7. Theoretical Probability: The ratio of the number of favorable outcomes to the total number of possible outcomes.

Formula: P(E) = $\frac{Numberoffavorableoutcomes}{Totalnumberofpossibleoutcomes}$

Key Points:

• The probability of any event lies between 0 and 1 (inclusive).
• The sum of probabilities of all possible outcomes of an experiment is 1.
• Experimental probability may vary with the number of trials, but as the number of trials increases, it tends to approach theoretical probability.

3.0Key Features of the NCERT Solution of Introduction to Probability

1. Basic Definitions and Concepts:

• Introduces fundamental terms such as random experiments, sample space, events, and outcomes.
• Provides real-life examples for better understanding.

2. Real-World Applications:

• Problems based on coin tosses, dice rolls, and drawing cards to connect probability with practical scenarios.

3. Use of Sample Space:

• Emphasis on listing all possible outcomes for different experiments.
• Demonstrates how to identify favorable outcomes for an event.

4. Step-by-Step Exercises:

• A variety of examples and exercises, ranging from simple to moderately challenging.
• Questions focus on scenarios like picking colored balls, rolling dice, or predicting outcomes.