---
title: "Sample space, event, outcome definitions"
subject: "Probability and Statistics"
chapter: 1
key: "semester_5/probability_and_statistics:sample-space-event-outcome"
source: https://www.bctengineer.com/q/semester_5/probability_and_statistics/sample-space-event-outcome
site: BCT Engineering
---

# Sample space, event, outcome definitions

Probability and Statistics · Chapter 1: Descriptive Statistics and Basic Probability

- Asked in: 2068 Jestha (old course), 5 marks
- Video: [Probability Vocabulary Explained : "Experiment", "Outcome", "Sample Space", "Event" and an Example](https://www.youtube.com/watch?v=0irL1gDCrq4) — Sulock Math
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/probability_and_statistics/sample-space-event-outcome
- Whole chapter: https://www.bctengineer.com/md/semester_5/probability_and_statistics/chapter-1

## Question

Define sample space, event and outcome of an experiment with suitable example.

## Short answer

Experiment: uncertain process. Outcome: single result (e.g., die shows 5). Sample space: set of all outcomes (e.g., {1,2,3,4,5,6}). Event: subset of sample space (e.g., {5,6} for >4).

## Answer

#### Experiment
An **experiment** is a process that gives a result which cannot be predicted with certainty. Example: throwing a die.

#### Outcome
An **outcome** is a single possible result of an experiment. Example: when a die is thrown, getting "4" is one outcome.

#### Sample space
The **sample space** (S) is the set of all possible outcomes of an experiment. Each element of S is a sample point.

- Tossing a coin: S = {H, T}
- Throwing a die: S = {1, 2, 3, 4, 5, 6}
- Tossing two coins: S = {HH, HT, TH, TT}

#### Event
An **event** is any subset of the sample space, that is, a collection of one or more outcomes. It occurs when the outcome of the experiment belongs to it.

- Simple event: contains one outcome, such as A = {4}.
- Compound event: contains more than one outcome, such as B = {2, 4, 6} ("an even number").

#### Example together
Experiment: throwing a die once.

| Term | Example |
|---|---|
| Outcome | 5 |
| Sample space | S = {1, 2, 3, 4, 5, 6}, n(S) = 6 |
| Event | E = "number greater than 4" = {5, 6} |
| Probability of E | n(E)/n(S) = 2/6 = 1/3 |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which is an outcome of throwing a die?
   A. Getting a number above 6
   B. {1,2,3,4,5,6}
   C. Getting an even number
   D. Getting 4
   Answer: D. An outcome is a single possible result. (Key point: Outcome)

2. What is the sample space of tossing two coins?
   A. {HH, TT}
   B. {H, T}
   C. {HT, TH}
   D. {HH, HT, TH, TT}
   Answer: D. It lists all possible outcomes: 4 in total. (Key point: Sample space)

3. What is an event?
   A. A subset of the sample space
   B. A number only
   C. A single die
   D. Always the whole sample space
   Answer: A. An event is a collection of one or more outcomes. (Key point: Event)

4. For E = number greater than 4 on a die, what is P(E)?
   A. 1/3
   B. 1/2
   C. 1/6
   D. 2/3
   Answer: A. E = {5,6}, so 2/6 = 1/3. (Key point: Event probability)

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