---
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id: "66f15998e361cd99fe370f0f"
title: "Probability"
board: "CBSE"
curriculum: "CBSE"
class: "Class 11"
subject: "Mathematics"
book: "Mathematics"
chapter: "Probability"
chapter_slug: "probability"
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version: 1
last_updated: "2026-06-20"
---

# Probability
This chapter discusses the mathematical concept of probability, which quantifies the likelihood of various outcomes in random experiments. It begins with defining events in relation to sample spaces and continues to explore different types of events and the axiomatic framework of probability.

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## Knowledge Snapshot
| Field | Details |
| :--- | :--- |
| Class | Class 11 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Probability |
| Pages | 289-313 |

---

## Chapter Summary
### Short Summary
The chapter provides definitions and classifications of various types of events in probability, including simple, compound, mutually exclusive, and exhaustive events. It also introduces the axiomatic approach to probability.

### Detailed Summary
The chapter elaborates on the concept of events as subsets of a sample space, introducing different types of events such as impossible events (φ) and sure events (S). It explains how events can be categorized into simple events (with one sample point) and compound events (with multiple sample points). The algebra of events is discussed, covering operations such as union, intersection, and complementary events. Significant examples illustrate the definitions, including the axiomatic definitions of probability, exploring acceptable probability assignments, and providing insights into calculating probabilities for various events.

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## Topic-Wise Explanation
### Event
An event is defined as any subset \(E\) of a sample space \(S\). Examples include selecting subsets associated with specific outcomes from experiments.

### Algebra of events
This section covers operations between events. It discusses complementary events, unions, intersections, and differences between events, illustrating how events relate using set notation.

### Mutually exclusive events
Events that cannot occur simultaneously are termed mutually exclusive. For instance, the occurrence of an odd number excludes the occurrence of an even number.

### Exhaustive events
Events that collectively encompass all possible outcomes of a sample space are called exhaustive events. If events are also mutually exclusive, they form a group of mutually exclusive and exhaustive events.

### Axiomatic Approach to Probability
The axiomatic approach introduces three fundamental axioms that define the probability function, focusing on non-negativity, the total probability of the sample space being 1, and the additive property of mutually exclusive events.

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## Core Ideas
| Idea | Explanation |
| :--- | :--- |
| Event | A subset of the sample space \(S\). |
| Impossible event | The empty set \(φ\). |
| Sure event | The entire sample space \(S\). |
| Complementary event | \(A′\) representing 'not A', calculated as \(S - A\). |
| Mutually exclusive events | Events \(A\) and \(B\) are mutually exclusive if \(A ∩ B = φ\). |
| Exhaustive events | Events \(E_1, E_2, \ldots, E_n\) are exhaustive if \(E_1 ∪ E_2 ∪ ... ∪ E_n = S\). |
| Probability of an event | Given by \(P(E) = m/n\) for equally likely outcomes. |
| Probability of 'A or B' | \(P(A ∪ B) = P(A) + P(B) - P(A ∩ B)\). |
| Probability of 'not A' | Given by \(P(A′) = 1 - P(A)\). |

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## Important Points for Revision
* Definition and classification of events.
* Understanding the algebra of events with examples.
* Characteristics of mutually exclusive and exhaustive events.
* Axioms of probability and their implications in calculating event probabilities.
* Understanding how to calculate probabilities in various scenarios.
* The importance of the sample space in probability.

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## Vocabulary and Glossary
| Word / Phrase | Meaning |
| :--- | :--- |
| Sample space | The set of all possible outcomes of an experiment. |
| Event | A subset of a sample space. |
| Mutually exclusive | Two events cannot occur at the same time. |
| Exhaustive events | Events that cover all possible outcomes. |
| Axiomatic approach | A method of defining probability based on foundational axioms. |

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## Practice Questions
### Short Answer Questions
1. What is a sample space?
2. Define a simple event.
3. Explain mutually exclusive events with an example.
4. What is an exhaustive event?
5. State the axioms of probability.

### Long Answer Questions
1. Describe the algebra of events and provide examples of each type of event operation.
2. Discuss the axiomatic approach to probability and its significance in probability theory.
3. Illustrate with examples how to find the probability of an event using its associated sample space and outcomes.

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## Related Concepts
* Random experiment
* Probability distributions
* Set theory concepts relevant to events and probabilities.

---

## Source Attribution
| Field | Value |
| :--- | :--- |
| Source | Edzy |
| Reference Type | examSubjectBookChapter |
| Reference ID | 66f15998e361cd99fe370f0f |
| Canonical URL | https://www.edzy.ai/cbse-class-11-mathematics-probability |
| Markdown URL | https://www.edzy.ai/okf/chapter/cbse-class-11-mathematics-probability.md |