Class 9 Math Chapter 13: All Notes & Resources
Choose a resource below for Chapter 13 Probability, from solved exercises to definitions and MCQs.
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Class 9 Mathematics Chapter 13 introduces the fundamental concepts of probability, the branch of mathematics that deals with the likelihood of events occurring. You will learn to calculate the probability of single events, understand sample spaces, and apply relative and expected frequency to real-life situations. This hub gathers every Chapter 13 resource in one place. Start with the Chapter 13 definitions for quick revision, then move to the solved exercises below. For targeted practice, try the Chapter 13 MCQs. You can also review the Grade 9 Math Pairing Scheme to understand paper weightings. When you are done, return to the main Class 9 Mathematics page for the next chapter.
Last updated: October 23, 2026
Exercise 13.1 Solved
Calculate probabilities of single events using dice, cards, coins, and word problems, and find the probability of complementary events.
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Exercise 13.2 Solved
Find the relative frequency of given data and calculate expected frequencies for repeated experiments.
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Review Exercise 13
Comprehensive mixed problems covering the entire chapter, including multiple-choice questions and real-life applications of probability.
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Chapter 13 Definitions
All key definitions and formulas including sample space, event, probability, relative frequency, and expected frequency.
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Chapter 13 MCQs
Multiple-choice questions covering the entire chapter with detailed solutions, perfect for exam preparation and self-testing.
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Muhammad Tayyab
Subject Specialist Math
MSc Mathematics · Govt Christian High School Daska, Sialkot, Punjab
Last updated: October 23, 2026
Key Concepts – Probability
Probability of an Event
\(P(A) = \frac{n(A)}{n(S)}\)
The ratio of favorable outcomes to the total number of possible outcomes.
Complementary Event
\(P(A') = 1 - P(A)\)
The probability of an event not occurring is 1 minus the probability that it does occur.
Relative Frequency
\(\frac{f}{N}\)
The number of times an event occurs divided by the total number of trials.
Expected Frequency
\(E = N \times P(A)\)
The total number of trials multiplied by the probability of the event occurring.
Range of Probability
\(0 \leq P(A) \leq 1\)
The probability of any event is always between 0 and 1 (inclusive).
Deck of Cards
\(n(S) = 52\)
A standard deck has 52 cards: 4 suits of 13 cards each, with 26 red and 26 black cards.
Chapter 13 Frequently Asked Questions
What is probability?
Probability is a measure of the likelihood that a particular event will occur. It is calculated as the number of favorable outcomes divided by the total number of possible outcomes.
What is a sample space?
The sample space is the set of all possible outcomes of an experiment. For example, when tossing a coin, the sample space is {Head, Tail}.
What is the complement of an event?
The complement of an event A, denoted as A', is the event that A does not occur. The probability of the complement is \(P(A') = 1 - P(A)\).
What is relative frequency?
Relative frequency is the ratio of the number of times an event occurs to the total number of trials. It is an estimate of the probability of the event when an experiment is repeated many times.
What is expected frequency?
Expected frequency is the number of times you would expect an event to occur in a given number of trials, calculated by multiplying the total number of trials by the probability of the event.
Created by Hira Science Academy | Aligned with Punjab Board 2027 Syllabus