Chance And Probability: Events, Formula & Examples

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Chance and Probability are used to interpret the possibility of the occurrence of some event. In mathematics, the term chance which indicates the possibility is called probability. Probability plays an essential role in various fields like scientific research, mathematics calculations(statistics), sports, weather forecasting, medical, technical(computer games), engineering, finance etc. Probability usually represents the occurrence of different events. Probability is used to determine the prediction of things that are likely to occur.

Read More: Independent Events

Table of Contents

What do you mean by Chance and Probability?
Terminology used for Probability
Types of Events
Types of Probability
Applications of Probability
Things to Remember
Sample Questions

Key takeaways: Probability, Chance, Random Experiment, Event, Sure Event, Sample Space

Chance and Probability

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Chance is defined as the possibility of something happening. In mathematics, the chances of something occurring is known as probability. Probability is defined as the possibility of the occurrences of events. The values of probability lie between 0 and 1. Probability is denoted as P or P(A).

Mathematically,

0 ≤ P(A) ≤ 1

Where,

P(A) ⇒ The probability of favourable event.

0 ⇒ The probability of impossible event or uncertain event.

1⇒ The probability of possible event or certain event.

Probability Range Diagram

Probability Range Diagram

Formula for Probability

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Probability is used to predict the possibility of an event. Probability formula is given by the ratio of favourable outcomes to the total number of outcomes. Mathematically,

P(E) = Number of favourable outcomes / Total number of possible outcomes

Apart from this, there are some real-life examples of Probability:

Weather forecasting
Playing cards
Winning or losing a lottery
Flipping a coin
Throwing a dice
Average of batting in cricket

Probability

Probability

Also Read: Linear Programming

Important terms used in Probability

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To clearly understand probability, we need to have knowledge about certain terms which are discussed below:

Experiment: Anything that is going to happen is known as an experiment. It is also known as trial. For example: flipping a coin, throwing a dice etc.
Sample Space: Sample space is defined as the set of all the possible outcomes of an experiment. E.g. The sample space of a coin is 4 {HH, HT, TH, TT}.

Sample Space and Event

Sample Space and Event

Event: Event is used to represent the collection of the outcomes of a random experiment or subset of any sample space. E.g. The outcome of tossing a coin whether its head or tail is known as an event.
Outcome: Outcome is defined as the result of an experiment. E.g. when tossing the coin and getting a head as a result.
Random Experiment: Any experiment whose outcome is not predicted in advance is known as a random experiment. E.g. rolling a dice.

Also Read:

Geometric Probability	Sum of Probabilities	Elementary Event
Independent Events in Probability	Multiplication Theory on Probability	Conditional Probability Formula

Types of Events

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If there is something likely to happen it is known as an event in probability. Events are usually classified into four kinds which are mentioned below:

Elementary Events: In probability theory, any event which contains a single outcome in the sample space is known as an elementary event. It is also known as a single event.

Complementary Events: In probability theory, complementary events are those events which can or cannot occur. In other words, complementary events define the situation of whether an event will occur or not such as whether it will rain or not, whether guests come to your house or not. It is denoted as P(A’) or P(AC). Mathematically,

P(AC) = 1 - P(A)

Where,

A is the event which occurs.

Impossible Events: In probability theory, Impossible events are those events whose possibility to occur is negligible. Impossible event has a probability value of zero(‘0’).

Sure Events: In probability theory, certain events are known to be sure events. These kinds of events are guaranteed to occur. Sure events have a probability value of one (‘1’).

Different Probability Events Diagram

Different Probability Events Diagram

Also Read: Experimental Probability

Applications of Probability

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Probability is used in many fields such as medical, finance, industry, engineering, statistics, research and many more. Some of the important applications of probability are mentioned below:

In real life, probability theory is used in risk assessment and modelling.
In Insurance Industry and market trading, pricing and trading decisions are done on the basis of probability theory especially on actuarial science.

Applications of Probability

Applications of Probability

The probability methods are widely used by the government for environmental regulations, financial regulation and entitlement analysis.
In engineering, probability methods are used for analysing model parameters, measuring uncertainty of models etc.
In medicine, nurses and doctors use probability theory to find out the proportion of dosage as well as the risk of illness.
In genetics, probability theory is used to determine patterns of the inheritance of a trait as well as family illness that comes from forefathers.
In machine learning, probability theory is used to predict how much data a machine can store.
In the modern communication system, probability theory is used to design the system as well as to predict the error and noise.

Read more: Empirical Probability Formula

Things to Remember

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Probability is used to determine the possibility of the occurrence of an event.
Probability values lie in between ‘0’ and ‘1’.
Probability value of certain or sure events is 1.
Probability value of not happening or impossible event is 0.
Complement event is equal to the not of the event.
We can only find out the probability of those events whose total number of outcomes we already know.
Probability has extensive use in various fields such as weather forecasting, medical, finance, marketing and trading, communication, gaming, machine learning etc.
Elementary events are singleton in nature.

Also Read:

Sure Event	Theoretical Probability	Multiplication Rule of Probability
Probability Mcqs	Uniform Distribution formula	Invertible Matrix

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Sample Questions

Ques. What do you mean by Probability? Write down its formula? [2 marks]

Ans. Probability basically tells us whether the event will occur or not. In Mathematics,the chances of occurrence of any situation or event is known as probability. Probability has a range between 0 and 1. The value of probability does not exceed one. The concept of probability does not apply on those experiments or trials whose total outcome is unknown. Probability is denoted as P(event). Mathematically,

P(E) = Number of favourable outcomes / Total number of possible outcomes

Moreover, probability is defined as the ratio of the favourable outcomes to the total number of possible outcomes of an experiment.

Ques. What is the probability of a die coming up with the number less than 7? [3 marks]

Ans. Given, every face of a die is marked with a number less than 7. So, it is clear that we will always get a number less than 7 i.e. this is a sure event.

We know, dice have six sides. So, the possible trials are 6.

Now, probability of a sure event is(getting a number less than 7 is given by,

P(getting a number <7) = Number of favourable outcomes / Total number of possible outcomes

P(getting a number <7) = 6 / 6

P(getting a number <7) = 1.

Therefore, the probability of getting a number less than 7 or sure event is 1.

Ques. A die is thrown once. What is the probability of getting an odd number? What is the probability of not getting an odd number? [3 marks]

Ans. Given, A single time dice is thrown. We all know that dice have 6 sides.

Odd numbers on dice = 1,3,5.

So, the favourable outcomes = 3.

And, the total number of possible outcomes = 6.

Therefore, the probability of getting an odd number is given by

P(getting an odd number) = Number of favourable outcomes / Total number of possible outcomes

P(getting an odd number) = 3 / 6

P(getting an odd number) = ½

We know, not getting an odd number is the complement of getting an odd number. So, to find out the probability of the complement event below mentioned formula is used.

Now,

P(not getting an odd number)= 1 - P(getting an odd number)

P(not getting an odd number)= 1 - ½

P(not getting an odd number)= ½

Therefore, the probability of getting an odd number and not getting an odd number is ½ respectively.

Ques.When one card is drawn from a well shuffled deck of 52 cards. What is the probability of drawing a spade? [2 marks]

Ans. Given, a pack of 52 cards which is divided into four sections like spades, suits, hearts, diamonds and clubs. Also, each section has 13 cards.

So, the favourable outcomes = 13

And, total number of possible outcomes = 52

The probability of drawing a spade is given by,

P(drawing a spade) = Number of favourable outcomes / Total number of possible outcomes

P(drawing a spade) = 13 / 52

P(drawing a spade) = ¼

Therefore, the probability of drawing a spade is ¼.

Ques. In a class of 40 students, there are 25 boys and the rest are girls. From them, a class representative has to be selected. What is the possibility of selecting a girl student as a representative? [2 marks]

Ans. Given,

Total students = 40

Number of boys= 25

Then, number of girls = total students - number of boys

Number of girls = 40 - 25

Number of girls = 15

Since, the favourable outcome for a girl student = 15

Now, the probability of girl representative is given by,

P(girl representative) = Number of favourable outcome / Total number of possible outcome

P(girl representative) = 15/40

P(girl representative) = ?

Therefore, the probability of girl representative out of 40 students is ?.

Ques. One card is drawn from a well shuffled deck of 52 cards. Find out the probability following:

(i) an ace card?

(ii) a red ace card? [3 marks]

Ans. Given, a pack of 52 cards has 4 ace cards.

(i) So, the favourable outcomes = 4

Also,

Total number of possible outcomes is equal to the well shuffled deck of cards(i.e. 52)

Now, the probability of drawing an ace card is given as,

P( drawing a ace card) = the favourable outcomes / Total number of possible outcomes

P( drawing a ace card) = 4/52

P( drawing a ace card) = 1/13

Hence, the probability of drawing an ace card is 1/13.

(ii) We know, there are 2 red ace cards in all four ace cards.

So, the favourable outcomes = 2

And, total number of possible outcomes= 52

Now, the probability of getting a red ace card is given by,

P( drawing a red ace card) = the favourable outcomes / Total number of possible outcomes

P( drawing a red ace card) = 2/52

P( drawing a red ace card) = 1/26

Therefore, the probability of drawing an ace card is 1/26.

Ques. There is a bag which consists of 3 red balls, 5 black balls and 4 white balls. One ball is drawn at random. Find out the probability that it is a ball of colour. [5 marks]

(i) Red

(ii) black

(iii) White

(iv) Red or black

(v) Yellow

Ans. Given, when a random ball is drawn then any ball may come from all balls.

Hence, total number of balls = Red balls + Black balls + White balls

total number of balls = 3+5+4

total number of balls = 12

Hence, total number of possible outcomes = 12

(i) For Red Ball:-

Number of favourable outcome = 3

Now, the probability for drawing a red balls is given as,

P( drawing a red ball) = Number of favourable outcomes / Total number of possible outcomes

P( drawing a red ball) = 3/ 12

P( drawing a red ball) = ¼

Therefore, the probability of drawing a red ball is ¼.

(ii) For Black Ball:-

Number of Favourable outcome = 5

Now, the probability for drawing a black balls is given as,

P( drawing a black ball) = Number of favourable outcomes / Total number of possible outcomes

P( drawing a black ball) = 5/ 12

Therefore, the probability of getting a black ball is 5/12.

(iii) For White Ball:-

Number of favourable outcome = 4

Now, the probability for drawing a red balls is given as,

P( drawing a white ball) = Number of favourable outcomes / Total number of possible outcomes

P(drawing a white ball) = 4/ 12

P( drawing a white ball) = ?

Therefore, the probability of drawing a white ball is 1/3.

(iv) For Red or Black colour ball:-

Number of favourable outcome = red balls+black balls

Number of favourable outcome = 3+5

Number of favourable outcome = 8

Now, the probability for drawing a red or black ball is given as,

P( red or black ball) = Number of favourable outcomes / Total number of possible outcomes

P( red or black ball) = 8/ 12

P( red or black ball) = ?

Therefore, the probability of drawing a red or black ball is ?.

(v) For Yellow colour ball:-

We know that there is no yellow ball contained in the given bag.

So, Number of favourable outcome = 0

Now, the probability for drawing a yellow ball is given as,

P( yellow ball) = Number of favourable outcomes / Total number of possible outcomes

P( yellow ball) = 0/12

P( yellow ball) = 0

Therefore, the probability of drawing a yellow ball is 0.

Ques. A coin is tossed once. Write down the sample space. Also, find out the total number of events. [2 marks]

Ans. Given, a coin is tossed once. A coin has two sides such as head, tail.

Now, the sample space is given as,

S = {H,T} , where H = indicates the head and T= indicates the tail.

Also, the number of events = collection of possible outcomes

Number of events = 4

Therefore, the total number of events is 4.

Ques. A bag consists of 4 green balls and 2 yellow balls. Without looking into the bag, a random ball is drawn. Find out the probability of drawing a green ball? Is it more or less than drawing a yellow ball? [3 marks]

Ans. Given, total possible outcomes= green balls + yellow balls

total possible outcomes= 4+2

total possible outcomes= 6

And, favourable outcome of green ball = 4

Now, the probability of drawing a green ball is given as,

P(drawing a green ball) = number of favourable outcome / Total number of possible outcome

P(drawing a green ball) = 4/6

P(drawing a green ball) = ?

Therefore, the probability of drawing a green ball is ?.

Also, the favourable outcome o yellow ball = 2

Now, the probability of drawing a yellow ball is given as,

P(drawing a yellow ball) = number of favourable outcome / Total number of possible outcome

P(drawing a yellow ball) = 2/6

P(drawing a yellow ball) = ?

So, it is clear that the probability of drawing a green ball is more than that of a yellow ball.

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Chance And Probability: Events, Formula & Examples

Chance and Probability

Formula for Probability

Important terms used in Probability

Types of Events

Applications of Probability

Things to Remember

Previous Year Questions

Sample Questions

CBSE X Related Questions

1.
If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

2.
A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

3.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

4.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

5.
The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

6.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

Similar Mathematics Concepts

Comments

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Chance And Probability: Events, Formula & Examples

Chance and Probability

Formula for Probability

Important terms used in Probability

Types of Events

Applications of Probability

Things to Remember

Previous Year Questions

Sample Questions

CBSE X Related Questions

1.If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

2.A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

3.Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent. Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

4.An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

5.The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

6.A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

2.
A chord of a circle, of radius 14 cm, subtends an angle of $60^\circ$ at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

3.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

4.
An arc of length $2.2\text{ cm}$ subtends an angle $\theta$ at the centre of the circle with radius $2.8\text{ cm}$. The value of $\theta$ is

5.
The value of p for which roots of the quadratic equation $x^2 - px + 6 = 0$ are rational, is

6.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.