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# Probability Class 10 Notes CBSE Maths Chapter 15 (Free PDF Download) Last updated date: 02nd Dec 2023
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## Exam - Focused Revision Notes for CBSE Class 10 Maths Chapter 15 - Probability

CBSE Class 10 Maths Notes Chapter 15 Probability provided by Vedantu gives step by step explanation of topics included in the chapter. Access our most preferred study material, Probability Class 10 Notes, online, to quick-learn concepts on probability. Class 10 Probability Notes discusses a theoretical and experimental approach that can be conveniently learned and practiced to excel in your upcoming CBSE Board Exams. Vedantu is a platform that provides free CBSE Solutions and other study materials for students. You can download NCERT Solutions Class 10 Maths to help you to revise the complete Syllabus and score more marks in your examinations. Subjects like Science, Maths, English will become easy to study if you have access to NCERT Solution for Class 10 Science, Maths solutions, and solutions of other subjects that are available on Vedantu only.

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## CBSE Class 10 Maths Notes Chapter 15 Probability PDF

One of the main strategies that students should follow while preparing for their exams dictates that students should first complete comparatively easy chapters that require a lot of practice. Probability is one of those chapters. This is why today we are going to discuss class 10 maths chapter 15 revision notes in detail.

### What Do You Understand by Probability?

Let’s begin the class 10 maths notes of probability with the basic definition. According to experts, probability simply means possibility. It can be defined as the branch of mathematics that particularly deals with the occurrence of events that are random.

There are many revision notes for class 10 maths chapter 15 that states that the value of probability can be expressed from zero to one. One can also state, in other words, that probability is the extent to which an event is likely to occur. This is also known as the basic probability theory, which is used in the probability distribution.

Many class 10 revision notes probability also states that if a student wants to find out the probability of an event, then it is vital to first find out the total number of all possible outcomes. It should also be noted here that the probability of all the events in a sample space adds up to 1.

There is also a probability formula that one can use to calculate the probability of events that consist of complicated numbers. This formula can be explained as the possibility of an event that has to happen is equal to the ratio of the number of all favourable outcomes and the total number of outcomes. The same definition is also mentioned in other class 10 revision notes maths ch 15.

In other words, the Probability of an event that has to occur, P (E) = Number of favourable outcomes / Total number of outcomes

It should be noted here that sometimes students make mistakes between ‘favourable outcome’ and ‘desirable outcome.’ In this maths class 10 probability notes, we are mentioning that this is only a basic formula. There are also other variations of this formula that can be found in other notes of class 10 revision notes chapter 15.

### The Probability of an Event

Now, let’s move to the topic of the probability of an event. Begin by assuming that an event E can occur in r number of ways. This is out of a sum of n probable or possible equality likely ways. Based on this information, the probability of happening of the event or its success can be depicted as:

P (E) = r / n

The probability of that event not occurring is known as a failure. And the value of failure can be depicted as:

P (E’) = (n - r) / n = 1 - (r / n)

In this equation, E’ the fact that the event will not take place.

Hence, it can be said that:

P (E) + P (E’) = 1

Therefore, it can be concluded that the total number of all probability in any random experiment or test is equal to 1.

### Probability Class 10 – In a Nutshell

Probability is one of the significant chapters included in Class 10 books to impart knowledge of the concept amongst students. Probability, in other words, is the number of possible outcomes of occurrence of an event. Here,

• 0 depicts that the outcome is impossible

• One depicts certainty.

In Probability Class 10 Introduction, you will be familiarised with these concepts, precisely. After gaining knowledge of the ideas, solving probability questions in exams will get convenient for you.

Students struggling with the concept, or looking for a quick brush-up of the topic, will find our Probability Class 10 Notes beneficial. Equipping yourself with study material like this can help you acquire a thorough understanding of the topic considering that our subject experts, who have drafted it, have a complete understanding of student-requirement.

Besides, our study materials are convenient to download in PDF formats and can be accessed online as well. Now get thorough knowledge of probability and its concepts with our Probability Class 10 Notes.

## Class 10 Probability – Revision Notes

Skimming through the crucial topics is what every student does as a part of the last-minute study. Now, this last-minute study is made easier with our Probability Notes Class 10. You can read the critical topics just before the exam and excel in your academic venture.

• ### Notes of Probability Class 10 – Random Experiment

In this chapter of Probability, you will learn in detail about the random experiments performed and the associated probability of getting a particular outcome. So, you will be explained how there can be different outcomes if a single experiment is repeated several times, and these repetitions are termed as ‘trials’.

Therefore, the probability of an event to occur during an experiment is equal to:

The ratio of the number of outcomes in which there is a possibility of occurrence of the event/The total number of outcomes.

It will need you to understand the experiment and calculate two things first to be able to compute the probability of an event,

1. Total number of outcomes possible for the experiment

2. Total number of outcomes for which the event occurs

While this can be a time-consuming topic to understand, our Probability Class 10 Notes will make the process easier for you. With crisp and quality notes explaining the intricacies of probability, it will get easier to understand and solve questions by acquiring profound knowledge.

We assure the easiness in understanding because our Probability Class 10 Notes are prepared by highly qualified expert teachers from renowned universities who leave no stone unturned in preparing nothing but the best study material. Our quality study help is the much-needed assistance that can bring you better academic results.

• ### Probability 10th Class Notes – Different Kinds of Events

Chapter 15 on probability discusses the various events and its possibilities which are imperative for you to understand. Consequently, you can solve the exercise questions of a chapter with accuracy sans consuming much time.

So, when an experiment is performed it is likely that it can have certain events depending upon its occurrences. Probability Class 10 Notes will help you learn simplified definitions of these events and its usage in the experiment.

Following Are Some of the Terms Related to Events That You Will Be Dealing With, to Seek Answers to Questions.

1. Compound Event – In a random experiment, an event is termed as a compound event, if it is obtained by combining two or more elementary events which are also connected with the random experiment. So, compound events are the ones that have more than one possible outcome in a random experiment.

2. The Occurrence of an Event – It is considered that an event has occurred in a random experiment if any of the corresponding elementary events is the outcome of the random experiment.

3. Impossible Events – Such events which never occur are considered as impossible events, and the probability of its occurrence is zero.

For Example:

There is a bag of balls containing three green balls and two red balls. Now, you have to determine the probability of an event when you take out one green ball and one blue ball.

In this case, the probability of occurrence of the event is zero as there is no blue ball in the bag. So, for no possible outcomes, this event is possible.

Concepts such as these will get easier to understand if you study with our Probability Class 10 Notes.

1. Sure Event – A particular event is a specific event that will occur, so its probability is 1.

For Instance

The probability of finding a number greater than zero on throwing a die is always one because all the numbers are greater than 1.

Such events are called a sure event, which is certain to happen.

You will need to get familiar with such terms to ensure that you have a better understanding of the topic. Such grasp over the topic ensures that you are almost sure to perform better in your upcoming exams.

In this regard, accessing our Probability Class 10 Notes will provide you with the required knowledge. With our high-quality notes, you can secure higher marks in your academic pursuits in addition to the profound understanding of the chapter.

More often, students need a source of study material that they can rely on for the last-minute study, and Vedantu offers just that. With our Probability Class 10 Notes, you can quickly go through the concepts at the last-minute, and retain the terms explained in it briefly and in simple words that are easy to understand and learn.

Subsequently, in this chapter, the probability of occurrence of an event in a random experiment is calculated. The random experiment performed can be anything. However, three major categories of a random trial are included, such as Cards, Coins, and Die.

You will have to acquire a thorough knowledge of the experiments before you calculate the probability of such events as you can’t compute the probability of drawing a particular card from the deck of cards if you are not sure about the total number of cards in pack and about the number of a specific card in a pack. Therefore, follow our Probability Class 10 Notes to go further in the learning venture of cards, coins, and die.

• ### Class 10 Maths Probability Notes – Probability of Cards

A pack of cards has a total of 52 cards, and those are segregated in four suits –

2. Hearts (Red coloured)

3. Diamond (Red coloured)

4. Clubs (Black coloured)

Now, each suite contains 13 cards starting right from 1 to 13. However, fewer cards are named differently.

1. First Card - Termed as an ‘Ace’ and has a symbol of ‘A’ followed by a series of numbers starting from 2 to 10.

2. 11th card - Termed as ‘Jack’ and indicated by a symbol ‘J.’

3. 12th card - The ‘Queen’ and indicated with a symbol ‘Q.’

4. 13th card - A ‘King’ which has a symbol ‘K’ on it.

5. Jack, Queen, and King - Called face cards. Therefore, there are 12 face cards in a pack of 52 cards. Utilising this number, you can calculate the probability of an event’s occurrence.

6. Since the spades and clubs are black coloured and hearts and diamonds are red coloured, there are 26 black cards and 26 red cards.

Students can't understand and solve probability questions without acquiring proper information about the event. Getting familiar with the pack of cards will help you determine how many cards of a particular type are present in the pack. It assists in determining the total number of outcomes and the possible number of outcomes corresponding to the event in a random experiment.

You will be more equipped in terms of study help with our Probability Class 10 Notes to learn such concepts. You will be able to understand the intricacies of the topic or revise using our notes.

• ### Probability Chapter Class 10 PDF – Probability of Coins

Another kind of random experiment is associated with coins. Now, there can be two outcomes on the toss of a coin, either heads or tails. So, probability of getting tails or head on the toss of a coin will always be 1/2 as the total number of outcomes is 2, whereas there can be only one instance of the occurrence of heads or tails.

Further, students will have to acquire this information because compound events are asked where they have to deal with outcomes of two or more events. You will have to think of all possible outcomes to determine the probability of an event.

While these concepts require you to think critically, you may as well feel conceptually challenged because of the lack of understanding. Our Probability Class 10 Notes assist you with that as they bring the necessary information in the forefront. Subsequently, you don't have to invest more time in learning a particular concept.

Utilise our quality notes for acquiring a better understanding of advanced topics, learning steps to solve exercise questions and last-minute study. Our qualified expert teachers prepare study material that maintains standard as per the latest CBSE guidelines. Therefore, studying is more fun with Vedantu as your digital study companion.

• ### Probability Notes Class 10 – Probability of Die

Die has six faces with each face representing a number, starting from 1 to 6. So, the outcome of occurrence of any of the number starting from 1 up until 6 is equal.

It means that the probability of occurrence of 1 on a throw of dice is the same as the probability of occurrence of 4 on the throw of a dice. It stands true for any other number between 1 to 6. The probability for the occurrence of each such event will be 1/6.

Further, you will have to understand and analyse the number of such outcomes in an experiment of throwing two dice or three. You will have to analyse the number of such possible events in a random trial.

Therefore, referring our Probability Class 10 Notes will help you get thorough information of the concept of probability. You can glance through the topics last-minute and recapitulate the concepts efficiently to boost your academic performance.

Our Probability Chapter Class 10 PDF is an excellent study resource for students that provide pointwise notes on key topics important from exam perspective. You can access the below mentioned.

1. Learn the topics

2. Understand the procedure

To ensure ease of access, our revision notes are available online that is accessible anytime and from anywhere. Further, you can also download PDFs quickly in your device and revise with them. We aim to deliver quality assistance in the form of study material so that you can explore new heights of the academic venture.

### Fun Facts about Complementary Events

Did you know that complementary events are those events in which only two outcomes will happen that state whether an event will occur or not? For example, whether one of your friends will visit you or not, or whether you will get selected for a professional position or not.

It can also be said that complementary events are the events occurring in the exact opposite of whether the probable event will occur or not. Some more examples of complementary events are:

• Whether it will rain tomorrow or not

• Whether a student will pass his or her exams or not

• Whether you will win the lottery or not

### Benefits of Using Vedantu’s CBSE Class 10 Maths Notes Chapter 15

Do you know that there are many benefits of downloading CBSE class 10 maths notes from Vedantu? Some of those benefits are mentioned below.

• The notes can help students quickly revise important points before a test or exam

• These notes will help students in scoring better marks

• Notes are available in a pdf format, which is very easy to download

### Enrich your Learning with Vedantu

Vedantu is a single-stop solution for students as it provides revision notes for all subjects and all classes segregated in a chapter-wise format. You can refer to our notes for acquiring a brief understanding of the chapter as it covers all the key topics which are crucial from the exam point of view.

You can either learn the topics briefly before the exam when you have less time at your disposal or brush up your knowledge right before an exam.

While probability being one of the essential topics of mathematics, you can better learn the chapters with our Probability Class 10 Notes and never lag in shaping up your academic skills. Taking into account the benefit of our readers, apart from our Probability Class 10 Notes PDF, we also offer revision notes for other subjects as well. Avail to excel and secure subject-best scores

Besides, you will learn the shortcut techniques well that can give you an in-depth concept of Probability and its functionalities.

Our notes are just a click away as you can download them quickly on your digital device.

## Conclusion

Vedantu's Probability Class 10 Notes for CBSE Maths Chapter 15 offer a comprehensive and well-structured resource for students seeking to master this fundamental concept. Through their free PDF download, Vedantu provides a valuable aid to learners, simplifying complex probability principles with clarity and precision. These notes enable students to understand probability's theoretical foundations and practical applications, enhancing their problem-solving skills. The user-friendly format and engaging examples ensure an enjoyable learning experience. Vedantu's commitment to providing high-quality educational materials empowers students to excel in their studies, instilling confidence and proficiency in probability, a skill that extends beyond mathematics into various real-world scenarios. By making these notes freely accessible, Vedantu exemplifies its dedication to fostering academic excellence for all.

## FAQs on Probability Class 10 Notes CBSE Maths Chapter 15 (Free PDF Download)

1. What are the different types of events?

There are three different types of events:

Certain events: These events are guaranteed to happen. For example, the sun will rise tomorrow.

Impossible events: These events can never happen. For example, a coin will land on heads and tails at the same time.

Random events: These events can happen or not happen, and the outcome is uncertain. For example, the outcome of a coin toss.

2. What is a theoretical approach to understanding probability according to Revision Notes of Chapter 15 of Class 10 Maths?

The coin example is best used to understand the concept of mathematical probability. We are all well aware that a coin can land in only one of two ways - head up or tail up. Each outcome can be deemed as likely to occur. Thus, there is a 50% chance of the coin landing on heads or landing on tails. This is a simple theoretical approach that can be used to understand the probability of an event.

3. What is the formula used to calculate probability according to Revision Notes of Chapter 15 of Class 10 Maths?

Classical probability of an event, denoted as P(E), is calculated by dividing the number of outcomes favourable to the event by the number of all possible outcomes of the experiment. Pierre Simon Laplace laid down the principles of this theory in 1795. To understand probability better, you should refer to Revision Notes of Chapter 15 of Class 10 Maths. These will help you build your concepts as well as score good marks in your exams.

4. Can you explain the difference between experimental and theoretical probability according to Revision Notes of Chapter 15 of Class 10 Maths?

The experimental probability is also called empirical probability. It describes an event based on what has actually happened. This is in contrast to the theoretical probability of the event which aims to predict what will happen on the basis of certain assumptions. As the number of trials in an experiment increases, it is safe to say that the experimental and theoretical probabilities are likely to end up being almost the same.

5. Why is Chapter 15 of Class 10 Maths important?

Probability has several real-life applications as well. Even in the field of computer science and engineering, probability plays a crucial role. Modeling and reconstruction of internet data is done mainly using the principles of probability. Network traffic is also modelled and an analysis of algorithms and graphs is made. Several upcoming modern AI tools also depend upon probabilistic analysis to handle speech recognition. A class 10 student interested in this field should definitely check out Revision Notes of Chapter 15 of Class 10 Maths.

6. How can I score well in Chapter 15 of Class 10 Maths important for my exams?

Any chapter in Maths requires thorough and continuous revision. You cannot solve the sums if you do not keep yourself in the habit of practicing questions. Be consistent and stick to your NCERT maths textbook. Solve as many previous year question papers as you can get your hands on. Ask seniors and teachers for any helpful advice and watch Vedantu math lectures in case you feel like you need expert assistance to prepare for Revision Notes of Chapter 15 of Class 10 Maths.