Elementary Event: Concept & Examples

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An elementary event is a type of event that contains only a single outcome in the sample space. Using the concept of set, it is a singleton. The event can be described as a list of random experiments while considering a potential sample size.

An elementary event is also known as an atomic event or sample point.
An event refers to a subset of the respective sample space.
It is part of the probability that is included in NCERT Class 10 Mathematics.
Probability, in simple terms, means how likely something will happen.
In other words, it refers to the likeness or occurrence of an event in numeric values of 0 or 1.

A probability of 0 indicates it is an impossible event, and a probability of 1 indicates there is a hundred per cent chance of an event occurring.

The sum of the probability of all the elementary events of any experiment is equal to one.
Most common example of the probability of a car being able to fly is zero.

P= Number of ways an event can occur / over the total number of events

Table of Content

What is an Elementary Event?
Event and Outcome
Important Terms and Formula
Things to Remember
Sample Questions

Key Terms: Elementary Events, Probability, Events, Number, Sample Space, Sample Description Space, Possibility Space, Outcome, Atomic Event, Complementary Event, Equally Likely Event, Experiment

What is an Elementary Event?

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An elementary event refers to any experiment when it consists of a single outcome in the sample space. It is also called an atomic event or a simple event. In other words, if there is only one element of the sample space in the set representing an event, then this event is called a simple or elementary event.

These events are used to define probability theories applied to the events in real-time.
They occur with probabilities that are between zero and one.
In the case of discrete probability, where sample space is finite, each elementary event is assigned a particular probability value.
However, in the case of continuous distribution, the value of these events is equal to zero.

Example of What is an Elementary Event?

Example: For example, if we toss a coin, then the sample space S = {Head, Tail}. Now the event of Head appearing on the die is simple and is given by E = {Head}.

Example 2: For example, throwing a dice, the possible outcome is getting 1,2,3,4,5 and 6. Sample space S = {1, 2, 3, 4, 5, 6}.

E = {1}, E = {2}, E = {3}, E = {4}, E = {5}, E = {6}.

Sum of probabilities of all elementary event = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6 = 6/6 = 1.

Elementary Event

Also Read:

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Conditional Probability	Independent Events in Probability	What is a Set?
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Event and Outcome

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A possible result of an experiment is the outcome. A good outcome statement should be measurable, specific, and realistic. It depends upon the value of probability and on an event that can have more than one possible outcome.

It is the result of an experiment or trial.
An event is a collection of all the possible outcomes.
In theory, the collection of all possible outcomes of a random experiment is called the sample space.
So, an event is any subset of a sample space.

The collection of all possible outcomes of a random experiment is called a sample space or, sample description space or possibility space. It is usually denoted by S.

Any subset E of the sample space S is called an event.

Example of Event and Outcome

Example 1: For example, rolling 1,2,3,4,5, and 6 on a die are all outcomes.

Example 2: For example, consider tossing a die. The sample space is S = {1, 2, 3, 4, 5, 6}. E = {2, 4, 6} is an event,

which can be described in words as” the number is even” and E = {1, 3, 5} is an event which can be described in words as” the number is odd”.

Important Terms and formulas

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The important terms and formulas are as follows:

Probability

Probability is a concept which numerically means the degree of certainty of the occurrence of events. It is obtained by dividing the required favourable outcomes by the total number of possible outcomes.

Its value is less than equal to one or greater than equal to zero.
The sum of all the events in the given sample space is equivalent to one.

Probability of occurrence of an event P(E) = Number of outcomes favourable to E / Total number of possible outcomes

Example of Probability

Example: There are 12 pillows in a bed, 4 are red, 2 are yellow and 6 is blue. What is the probability of picking a yellow pillow?

Ans: The probability is equal to the number of yellow pillows in the bed divided by the total number of pillows, i.e. 2/12 = 1/6.

Experiment

An operation that can produce some well-defined outcomes is called an experiment. It is a procedure that is used to verify a hypothesis. The value is determined on the basis of a series of events.

Example of Experiment

Example: Some sample spaces

A die is thrown once S = {1, 2, 3, 4, 5, 6}; n(s) = 6
Two dice are thrown together or die is thrown twice

S = n(S) = 6²

A coin is tossed once S = {H, T}; n(S) = 2
A coin is tossed twice or two coins are tossed simultaneously

S = {HH, HT, TH, TT}; n(S) = 4 =2²

A coin is tossed three times or three coins are tossed simultaneously

S = {HHH, HHT, HTH, THH, TTT, TTH, THT, HTT}; n(S) = 8 = 2³

Equally Likely Events

Equally likely events refers to the types of events that consists of two or more events which have an equal chance of occurrence. In other words, the events are said to be equally likely if none of them is expected to occur in preference to the others.

It can mathematically be represented as:

Probability of equally likely event: 1 / size of sample space

Example of Equally Likely Events

Example 1: Probability of getting selected in an examination.

Example 2: Most common include coin toss during cricket match in which you are equally likely to get heads or tails.

Complementary Event

A complementary event is a type of event in which only one outcome of an experiment can happen when the other does not. Both these events complement the other.

They are mutually exclusive and collectively exhaustive.
Let E be an event and (not E) be an event which occurs only when” E” does not occur.
The event (not E) is called the complementary event of E.

Then P(E) + P (not E) = 1

P(E) = 1 – P (not E) → 0 ≤ P(E) ≤ 1

The sum of probabilities of all elementary events of an experiment is always a unity i.e., equal to 1.

Example of Complementary Event

Example: A person who does not go to competition is a complement to someone who does.

If you get a yellow card, your compliment is to get a black card.

Things to Remember

Elementary event is a type of event that consists of a single outcome in the sample space.
It determines the information about the chances of occurrence for different studies and exclusive events.
The probability of an event occurring is the number of ways in which an event can occur over the total number of possible events.
Probability is the branch of mathematics that describes the likeness or occurrence of an event.
It is used to measure the degree of certainty in the function.
The outcome explains the random situation for a variety of events.

Also Read:

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Theoretical Approach of Probability	Events in Probability	Events and their Types in Probability

Sample Questions

Ques. Find the probability of getting a number less than 4 in a single throw of a die? (2 marks)

Ans: Possible outcome = {1, 2, 3}

∴ P (Getting a number < 4) = 3/6 = 1/2

Ques. If P(E) = 0.05, what is the probability of 'not E'? (2 marks)

Ans: \(\because \) P(E) + P (not E) = 1

∴ 0.05 + P (not E) = 1 ⇒ P (not E) = 1 – 0.05

= 0.95

Thus, probability of 'not E' = 0.95.

Ques. A bag contains 3 red balls and 5 black balls. A ball is drawn at random fret the bag. What is the probability that the ball drawn is (4 marks)
i) red?
ii) not red?

Ans: Total number of balls = 3 + 5 = 8

∴ Number of all possible outcomes = 8

For red balls:

\(\because \)There are 3 red balls.

∴ Number of favourable outcomes = 3

∴P _Red = Number of favourable outcome / Number of all possible outcome = 3/8

For not red balls:

Probability of the ball drawn which is not red

= 1-38=8-38= 58

Ques. A box contains 5 red marbles, 8 white marbles and 4 green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be (4 marks)
i) red? and
ii) white?
iii) not green?

Ans: Total number of marbles = 5 + 8 + 4 = 17

For red marbles:

\(\because \)Number of red marbles = 5

∴ Number of favourable outcomes = 5

∴ Probability of red marbles, P(red) = 517

For white balls:

\(\because \)Number of white balls = 8

∴ Probability of white balls,

P(White) = 817

For not green balls:

\(\because \)Number of white balls = 4

∴ Number of 'not green' balls = 17 – 4 = 13

i.e., Favourable outcomes = 13

∴ Probability of ball 'not green'

P(White) = 1317

Ques. A game of chance consists of spinning an arrow that comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6,7, 8 (see figure), and these are equally likely outcomes. What is the probability that it will point at: (4 marks)
i) 8?
ii) an odd number?
iii) a number greater than 2?

Ans: Total numbers marked = 8

When pointer points at 8:

Total number of outcomes = 8

Number of favourable outcomes = 1

∴ P ₍₈₎ = Number of favourable outcome / Number of all possible outcome = 18

When pointer points at an odd number:

Number of odd numbers from 1 to 8 = 4 [\(\because \) odd numbers are 1,3 ,5 and 7]

Number of favourable outcomes = 4

∴ P _(odd)= Number of favourable outcome / Number of all possible outcome = 48= 12

When pointer points at a number greater than 2:

Number of numbers greater than 2 = 6 [\(\because \) the numbers are 2,3,4,5,6,7 and 8]

Number of favourable outcomes = 6

∴ P _{(greater than 2)} = Number of favourable outcome / Number of all possible outcome = 68= 34

Ques. Two dice are thrown simultaneously. What is the probability of obtaining a total of 11? (2 marks)

Ans. The possible outcomes are for a sum 10 are -

{ 5, 6 }, and { 6, 5 }

The total no. of outcomes are 36

So, the probability of obtaining a total of 11 is 2 / 36 = 1 / 18

Ques. A bag contains both red and blue balls. If the probability of getting a red ball is 1/5. What is the probability of getting blue balls? (2 marks)

Ans. Since we know that both are complimentary events. Therefore P(red balls) + P(blue balls) = 1

So, P(blue balls) = 1-P(red balls)

= 1 - 1/5

=4/5

Ques. If P(E) = 0.01, what is the probability of 'not E'? (2 marks)

Ans: It is given that P(E) = 0.01

P(E) + P (not E) = 1
0.01 + P (not E) = 1 ⇒ P (not E) = 1 – 0.01
0.99

Thus, probability of 'not E' = 0.95.

Ques. Find the probability of getting a number less than 4 in a single throw of a die? (2 marks)

Ans. Possible outcome = {1, 2, 3}

∴ P (Getting a number < 4) = 3/6 = ½

Ques. A random number is chosen from 1 to 30. Calculate the probability of not choosing a perfect cube? (2 marks)

Ans. Let Z' be the event of choosing a perfect square. The sample space is given as follows:

Z' = {1, 8, 27}
Total number of outcomes = 30
Favorable outcomes = 3
P(Z') = 3 / 30.
P(Z) = 1 - (3 / 30)
1- 1/10
9/10

Ques. Two coins are flipped 80 times simultaneously. What is the probability of both coins landing on heads? (2 marks)

Ans. The possible outcomes - (H, H), (H, T), (T, H), and (T, T).

The no. of possible outcomes of both coins landing on heads is 1

So, the probability will be 1/4 or 25%.

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Elementary Event: Concept & Examples