Class 9 Mathematics Exercise 11.3 – Probability (Complete Explanation with Examples)

Probability is a key concept in Class 9 Mathematics that helps students understand how likely an event is to occur. Exercise 11.3 focuses on applying probability formulas to real exam-style problems, including sample spaces, relative frequency, and expected outcomes.

This exercise is important because it develops logical thinking and prepares students for advanced topics in statistics and decision-making.

Class 9 Mathematics Exercise 11.3 Probability showing solved examples and probability calculations for Federal Board exams

Basic Concept of Probability

Probability measures the chance of an event occurring. It is always a number between 0 and 1.

Probability Formula:

P(E) = Number of Favorable Outcomes / Total Number of Possible Outcomes

If an event is certain, its probability is 1. If it is impossible, its probability is 0.

Sample Space

The sample space is the set of all possible outcomes of an experiment.

Example: When tossing a coin, the sample space is {Head, Tail}.

Relative and Expected Frequency

Relative Frequency

Relative frequency is based on experimental results.

Formula:

Relative Frequency = Frequency of Event / Total Number of Trials

Expected Frequency

Expected frequency predicts how many times an event will occur.

Formula:

Expected Frequency = Probability × Number of Trials

Step-by-Step Solved Examples

Example 1: Letters of a Word

Find probability from the word ALLAH.

Total letters = 5

Vowels (A appears twice): P = 2/5
Letter H (1 occurrence): P = 1/5
Letter L (2 occurrences): P = 2/5
Consonants (L, L, H = 3): P = 3/5

This type of question checks your understanding of counting outcomes correctly.

Example 2: Factory Production

A factory produces:

7000 Jackets
2000 Sweaters
3000 Trousers

Total items = 12000

Faulty items = 18

Probability of selecting a trouser = 3000 / 12000 = 1/4
Probability of selecting a faulty item = 18 / 12000 = 3/2000

This example shows how probability is applied in real-life situations.

Example 3: Special Dice

A 10-sided dice has numbers: 4, 4, 4, 4, 5, 5, 6, 7, 8

P(4) = 4/10 = 2/5
Prime numbers (5, 5, 7): P = 3/10
Factors of 12 (4 and 6): total = 5 → P = 1/2

This type of question tests your ability to identify conditions within a sample space.

Example 4: Expected Frequency

If probability of getting heads is 3/5 and coin is tossed 520 times:

Expected heads = (3/5) × 520 = 312

If probability of getting 6 on a dice is 1/8 and rolled 6000 times:

Expected number of 6s = (1/8) × 6000 = 750

These questions are very common in exams and carry good marks.

Important Rules in Probability

The sum of probabilities of all outcomes is always 1
P(Event) + P(Not Event) = 1
Probability can never be negative
Impossible events have probability 0

Common Mistakes to Avoid

Incorrect counting of total outcomes
Forgetting to simplify fractions
Misinterpreting the question
Mixing up favorable and total outcomes

Careful reading and proper step-by-step working can prevent these errors.

Exam Tips for Exercise 11.3

Always write the probability formula first
Clearly define sample space
Show all steps for full marks
Simplify answers properly
Practice different types of questions

Examiners reward clear method and logical presentation.

Why This Exercise Is Important

Probability is not just a mathematical topic. It is used in science, business, and daily decision-making. Understanding this chapter improves analytical thinking and problem-solving ability.

Strong command over Exercise 11.3 helps in both board exams and higher-level mathematics.

Explore More Lessons

Find more Class 9 Mathematics notes, solved exercises, and concept-based lessons on the STEMBridge Learning platform.

Class 9 Mathematics Exercise 11.3 – Probability is essential for building a strong understanding of how events and outcomes are analyzed mathematically. With consistent practice and clear concepts, students can solve even complex questions with confidence.

STEMBridge Learning provides structured and exam-focused explanations to help students achieve better results.