Learn Event in Probability Explained with Examples

Aanchal SoniI’m a fun-loving TESOL certified educator with over 10 years of experience in teaching English and public speaking. I’ve worked with renowned institutions like the British School of Language, Prime Speech Power Language, and currently, PlanetSpark. I’m passionate about helping students grow and thrive, and there’s nothing more rewarding to me than seeing them succeed.

Last Updated At: 20 Apr 2026

11 min read

Table of Contents

What Is an Event in Probability?
What Is a Random Experiment in Maths?
What Is Outcome in Maths?
What Is the Outcome vs the Event?
What Is Event in Probability? A Full Definition
Event in Math — Types Explained with Examples
Sample Space and Events — How They Connect
Solved Examples: Event in Probability
Practice Worksheet: Events in Probability
Common Mistakes Students Make in Probability Events
How PlanetSpark Helps Students Master Probability
Wrapping Up
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You are tossing a coin. Will it land heads or tails? You roll a die. Will you get a six? These everyday situations are questions of probability — and the answer always depends on understanding one key idea: the event. Whether you are studying for Class 9, preparing for board exams, or just trying to make sense of a chapter that feels confusing, this guide will make it click.

In this blog, you will learn exactly what an event in probability means, what an outcome is, how sample space connects to events, and the different types of events with clear examples. PlanetSpark's Maths programme helps students build conceptual clarity on topics like probability through 1:1 coaching that focuses on understanding, not memorisation.

What Is an Event in Probability?

Event in Probability: An event in probability is a specific outcome or a set of outcomes from a random experiment. It is a subset of the sample space (the complete list of all possible outcomes). For example, when rolling a six-sided die, getting an even number (2, 4, or 6) is an event. The probability of an event is calculated as: P(E) = Number of favourable outcomes ÷ Total number of outcomes. Events can be simple (one outcome), compound (multiple outcomes), certain, impossible, independent, dependent, or mutually exclusive.

What Is a Random Experiment in Maths?

Before understanding what an event is, you need to understand what a random experiment means in mathematics.

A random experiment is any activity or process whose result cannot be predicted with certainty in advance, but all possible results are known. Classic examples include:

Tossing a fair coin — you know the result will be heads or tails, but you cannot predict which one.
Rolling a six-sided die — the result will be one of {1, 2, 3, 4, 5, 6}, but you do not know which before you roll.
Drawing a card from a shuffled deck — any of 52 cards could come up.

All probability problems are built around random experiments, and all events arise from them.

What Is Outcome in Maths?

An outcome is a single, specific result of a random experiment.

When you toss a coin once, there are two possible outcomes: Heads (H) and Tails (T). When you roll a die once, there are six possible outcomes: 1, 2, 3, 4, 5, and 6. Each of these individual results is called an outcome.

Outcome definition in maths: An outcome is any one of the possible results that can occur when a random experiment is performed.

It is important not to confuse an outcome with an event. An outcome is a single result. An event can be one outcome or a collection of outcomes that share a common condition.

Term	Definition	Example (rolling a die)
Outcome	A single result	Getting a 3
Event	One or more outcomes grouped by a condition	Getting an odd number: {1, 3, 5}
Sample Space	All possible outcomes	{1, 2, 3, 4, 5, 6}

What Is the Outcome vs the Event?

Students often mix up outcomes and events. Here is the cleanest way to understand the difference:

An outcome is what actually happens in one trial of the experiment.
An event is what you are looking for — it can match one outcome or several.

Example: You roll a die. The outcome is the specific number that comes up — say, 4. But the event "getting an even number" includes outcomes 2, 4, and 6. So outcome 4 satisfies this event. Outcome 3 does not.

Think of the event as a question and the outcomes as the possible answers. The event "getting a number greater than 4" is satisfied by outcomes 5 and 6.

What Is Event in Probability? A Full Definition

An event in probability is any subset of the sample space. In other words, an event is a collection of one or more outcomes from a random experiment that we are interested in observing or calculating the probability of.

Formal definition: If S is the sample space of a random experiment, then any subset E of S is called an event.

The probability formula for an event:

P(E) = Number of favourable outcomes ÷ Total number of outcomes

Example: A fair die is rolled. What is the probability of getting a prime number?

Sample space S = {1, 2, 3, 4, 5, 6}
Prime numbers on a die = {2, 3, 5}
Number of favourable outcomes = 3
Total outcomes = 6
P(E) = 3/6 = 1/2

Event in Math — Types Explained with Examples

There are several types of events in probability, each with its own properties and examples.

Simple Event

A simple event consists of exactly one outcome from the sample space.

Example: Rolling a die and getting a 5.

S = {1, 2, 3, 4, 5, 6}
E = {5}
P(E) = 1/6

Compound Event

A compound event consists of two or more outcomes from the sample space.

Example: Tossing a coin twice and getting at least one head.

S = {HH, HT, TH, TT}
E = {HH, HT, TH}
P(E) = 3/4

Sure Event (Certain Event)

A sure event is one that will definitely occur. Its probability is always 1.

Example: Rolling a die and getting a number less than 7.

Every possible outcome (1, 2, 3, 4, 5, 6) satisfies this condition.
P(E) = 6/6 = 1

Impossible Event

An impossible event can never occur. Its probability is always 0.

Example: Rolling a die and getting an 8.

No outcome in the sample space satisfies this.
P(E) = 0/6 = 0

Independent Events

Two events are independent if the occurrence of one does not affect the probability of the other.

Example: Tossing a coin and rolling a die.

The result of the coin does not change the probability of any number on the die.
P(Heads AND 4) = P(Heads) × P(4) = 1/2 × 1/6 = 1/12

Dependent Events

Two events are dependent when the outcome of one affects the probability of the other.

Example: Drawing two cards from a deck without replacing the first.

After removing the first card, only 51 cards remain. This changes the probability of the second draw.
The two draws are dependent events.

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Mutually Exclusive Events

Two events are mutually exclusive if they cannot both occur at the same time. If A happens, B cannot happen in the same trial.

Example: Rolling a die and getting both an even and an odd number in a single roll.

These cannot happen together.
P(A and B) = 0

Example of non-mutually exclusive: Drawing a card that is both a King and a Heart (King of Hearts satisfies both).

Complementary Events

The complement of an event E is the event that E does not occur. It contains all outcomes in the sample space that are not in E.

Formula: P(E') = 1 − P(E)

Example: Probability of NOT rolling a 6 on a die.

P(rolling a 6) = 1/6
P(not rolling a 6) = 1 − 1/6 = 5/6

Sample Space and Events — How They Connect

The sample space is the foundation of all probability questions. It is the complete set of all possible outcomes of a random experiment.

Sample space examples:

Experiment	Sample Space
Tossing one coin	{H, T}
Tossing two coins	{HH, HT, TH, TT}
Rolling one die	{1, 2, 3, 4, 5, 6}
Drawing a card	All 52 cards

Every event you work with in probability is a subset of its sample space. If an event includes all outcomes in the sample space, it is a sure event. If it includes none, it is an impossible event. Everything in between is a regular event with a probability between 0 and 1.

Solved Examples: Event in Probability

Example 1

A bag contains 3 red balls, 4 blue balls, and 3 green balls. One ball is drawn at random. Find the probability of drawing a blue ball.

Total outcomes = 3 + 4 + 3 = 10
Favourable outcomes (blue) = 4
P(blue) = 4/10 = 2/5

Example 2

Two coins are tossed. What is the probability of getting exactly one head?

S = {HH, HT, TH, TT}
Favourable outcomes = {HT, TH} = 2
P(exactly one head) = 2/4 = 1/2

Example 3

A die is rolled. What is the probability of getting a number divisible by 3?

S = {1, 2, 3, 4, 5, 6}
Divisible by 3: {3, 6} = 2 outcomes
P(E) = 2/6 = 1/3

Example 4

A card is drawn at random from a standard 52-card deck. What is the probability it is NOT a spade?

Total cards = 52, Spades = 13
P(spade) = 13/52 = 1/4
P(not a spade) = 1 − 1/4 = 3/4

Practice Worksheet: Events in Probability

Try these on your own. Answers are given below.

Q1. A fair die is rolled. Find the probability of getting a number greater than 4.

Q2. Two coins are tossed. Find the probability of getting at least one tail.

Q3. A bag has 5 red and 7 yellow marbles. One marble is picked at random. What is the probability it is yellow?

Q4. From a deck of 52 cards, one card is drawn. What is the probability of drawing a King?

Q5. Events A = {getting an even number on a die} and B = {getting an odd number on a die}. Are A and B mutually exclusive?

Answers:

P(greater than 4) = 2/6 = 1/3 (outcomes: 5, 6)
P(at least one tail) = 3/4 (outcomes: TH, HT, TT)
P(yellow) = 7/12
P(King) = 4/52 = 1/13
Yes — an even number and an odd number cannot occur together in a single roll. A and B are mutually exclusive.

Common Mistakes Students Make in Probability Events

Confusing outcome and event: Remember, an outcome is one result; an event is a set of results.
Forgetting that P(E) is always between 0 and 1: If you calculate a probability greater than 1 or less than 0, recheck your working.
Treating dependent events as independent: Always check whether the first event changes the conditions for the second.
Ignoring the sample space: Every probability question starts with listing the sample space correctly.

How PlanetSpark Helps Students Master Probability

Many students find probability confusing because it feels abstract. PlanetSpark's Maths programme makes it concrete through real-life examples, step-by-step concept coaching, and regular practice — all in a 1:1 setting where your child gets to ask every question they have.

1:1 Concept-Based Coaching — certified math experts focus on clarity, not rote memorisation
Step-by-Step Problem Solving — students learn to break down probability questions systematically
Gamified Practice Tools — interactive quizzes and puzzles reinforce concepts like events, outcomes, and sample space in an engaging way
AI-Powered Progress Tracking — instant feedback and adaptive difficulty so every session builds on the last
Real-Life Examples — probability concepts taught using coins, dice, cards, and everyday scenarios students can relate to
Regular Practice Sheets — structured homework and worksheets to reinforce learning between sessions

Wrapping Up

An event in probability is simply a set of outcomes from a random experiment that you are interested in. Once you understand the difference between an outcome and an event, build your sample space correctly, and know the different types of events — simple, compound, sure, impossible, independent, dependent, mutually exclusive, and complementary probability becomes one of the most logical and satisfying topics in school mathematics.

The formula P(E) = Favourable outcomes ÷ Total outcomes is the thread that runs through every question. Get comfortable with it. Practise regularly using the worksheet above. And if you want expert guidance to make sure every concept is clear before exam day, PlanetSpark's Maths programme is the right place to start.