NCERT Class 11 Mathematics Mathematics: Chapter 14 — Probability
This chapter introduces the fundamental concepts of Probability in Mathematics for Class 11 students under the CBSE curriculum. It begins by defining an 'event' as any subset of a sample space associated with a random experiment. The text illustrates this with examples like coin tosses, where specific outcomes (like getting exactly one head) form events. It further explains the 'occurrence of an event,' stating it happens if the experimental outcome is an element of the event set. The chapter categorizes events into 'impossible events' (represented by the empty set φ) and 'sure events' (represented by the entire sample space S), using die rolling examples. Finally, it defines 'simple events' as those containing only one sample point, noting that a sample space with n elements has n simple events. This foundational understanding is crucial for further study in probability and statistics.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 11 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 14 — Probability |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 693 |
Learning outcomes
- Define an event as a subset of a sample space.
- Understand the concept of the occurrence of an event.
- Differentiate between impossible, sure, and simple events.
- Relate events to subsets of the sample space in random experiments.
Vocabulary
| Word | Meaning |
|---|---|
| Random experiment | An experiment whose outcome cannot be predicted with certainty. |
| Sample space | The set of all possible outcomes of a random experiment. |
| Event | Any subset of the sample space. |
| Occurrence of an event | An event is said to occur if the outcome of the experiment belongs to the event set. |
| Impossible event | An event that cannot occur, represented by the empty set (φ). |
| Sure event | An event that is certain to occur, represented by the sample space (S). |
| Simple event | An event containing exactly one sample point. |
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Practice questions
- Define an event in the context of a random experiment. Answer: An event is any subset of the sample space associated with a random experiment.
- What is the difference between a sure event and an impossible event? Answer: A sure event is the entire sample space (S), meaning it is certain to occur. An impossible event is the empty set (φ), meaning it cannot occur.
- If you toss a coin twice, what is the sample space? Answer: The sample space is S = {HH, HT, TH, TT}.
- Give an example of a simple event when rolling a die. Answer: An example of a simple event is getting a '3' on the die, represented by the set {3}.
Practice MCQs
Q1. Which of the following represents an impossible event?
Explanation: The empty set (φ) represents an event that cannot occur, hence it is an impossible event.
Q2. An event is defined as:
Explanation: An event is formally defined as any subset of the sample space associated with a random experiment.
Q3. If , 2, 3, 4, 5, 6} for rolling a die, which is a sure event?
Explanation: The sure event is the entire sample space (S), which includes all possible outcomes.
Q4. How many simple events are there in the sample space , HT, TH, TT}?
Explanation: A simple event has only one sample point. In this sample space, {HH}, {HT}, {TH}, and {TT} are the four simple events.
Q5. If event E occurs, it means the outcome ω satisfies:
Explanation: The event E is said to have occurred if the outcome ω of the experiment is such that ω is an element of E (ω ∈ E).
Frequently asked questions
What is a sample space in probability?
A sample space is the set of all possible outcomes of a random experiment.
How is an event related to a sample space?
An event is defined as any subset of the sample space.
What does it mean for an event to occur?
An event occurs if the actual outcome of the experiment is one of the elements within that event's set.
What is the difference between an impossible event and a sure event?
An impossible event corresponds to the empty set (φ) and cannot happen, while a sure event corresponds to the entire sample space (S) and is certain to happen.
Can you give an example of a simple event?
When rolling a die, the event of getting a '5' is a simple event, represented by the set {5}.
Related resources
Important topics
Topics covered
NCERT Class 11 Mathematics — Mathematics — Chapter 14 — Probability. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.