Class 10 Mathematics Revision Notes for Probability of Chapter 15
Probability is a widely used concept that plays an essential role in the everyday life of humans. This concept dictates the discipline of statistical analysis. The part played by probability in the branch of modern science is the replacement of absolute certainty. This theory helps predict various events with the help of performing estimations and predictions. Different statistical methods help in estimating observations for further analysis. Therefore, statistical methods are heavily dependent on the basic theory of probability.
Class 10 Mathematics Chapter 15 Notes are available on the Extramarks website. These revision notes will efficiently provide a detailed step-by-step explanation of each chapter topic. Students will gain access to the simplified concepts of probability with the help of Class 10 Mathematics Chapter 15 Notes. It consists of theoretical and experimental approaches that will help you learn the basic concepts efficiently.
Class 10 Mathematics Revision Notes for Probability of Chapter 15
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CBSE Class 10 Mathematics Notes Chapter 15 Probability PDF
What Do You Understand by Probability?
The basic definition of probability entails that it is merely a possibility. It can be further defined as the sub-branch of Mathematics mainly dealing with the occurrence of randomly designed events.
The Class 10 Mathematics Chapter 15 Notes state that the value of probability can be widely expressed starting from zero to one. It can also be noted that probability is the extent to which any event can occur. This is known as the basic probability theory, which is utilised in probability distribution.
For instance, if a student is interested in searching for the probability of any event, it becomes necessary to find the total number of all the possible outcomes. It should be brought to your notice that the possibility of the sum of all the events in any sample space always adds up to 1.
The probability formula is used for calculating the probability of events which consists of complex numbers. The possibility of any event that will occur is equivalent to the ratio of numbers of all the favorable outcomes and the total outcomes. You can find a similar definition in other class 10 maths chapter 15 notes.
When rephrased, the probability of any event that can occur, P(E)= number of favorable outcomes/total number of outcomes.
It should be brought into notice that, at times, students confuse between ‘favourable outcome’ and ‘desirable outcome’. You will find the basic formula mentioned in the class 10 mathematics chapter 15 notes. Various variations of this formula are found in other notes of class 10 chapter 15 revision notes.
The Probability of an Event
Moving on to the next topic of the probability of an event, start by assuming that an event E occurs in r number of ways. This is the sum of n probable or possible equality likely ways. Based on the given information, the probability of any event is shown as:
P (E) = r / n
The probability of the event not occurring is called failure. The value of failure is shown as:
P (E’) = (n – r) / n = 1 – (r / n)
In this equation, E’ is the fact that the event will not occur.
Hence, it is safe to say that:
P (E) + P (E’) = 1
Hence, it is concluded that the total number of all possibilities in any random experiment or test is equal to 1.
Probability Class 10 – In a Nutshell
Probability is regarded as one of the highly significant chapters in Class 10 NCERT books to disseminate knowledge of the concept. In other words, the total number of possible outcomes of the occurrence of an event; here, 0 shows that the result is impossible, and one shows certainty.
In the introduction of Class 10 Probability, you will become familiar with the essential concepts with precision. After attaining information about the concepts, finding the solution to probability questions during exams will become an easy task for you.
Students who are struggling with this concept or are looking for a brush-up on the topic will undoubtedly find the Class 10 Mathematics Chapter 15 Notes helpful. Make yourself smarter by referring to this study material so that you can acquire a firm understanding of the essential topics that will come in the exam.
Moreover, the study material provided by Extramarks will make it convenient for you to learn, as it is available in PDF format too. This makes it convenient and accessible for you to study with total concentration.
Class 10 Probability – Revision Notes
Going through the vital topics will make a student confident, such that he or she can be convinced during last-minute preparation. Last-minute preparation will become convenient with the help of probability notes in Class 10. You can go through the essential topics right before the exam and further excel in your academic journey.
Notes of Probability Class 10 – Random Experiment
In the probability chapter, you will find a detailed explanation regarding the experiments randomly performed and the probability associated with achieving a particular outcome. So, you will get a firm grasp on how different results can be expected or predicted upon repeating a single experiment. These repetitions are called ‘trials’.
Therefore, the probability of an event occurring during an experiment is equal to:
The ratio of the number of outcomes with the possibility of occurrence of any event/ the total number of results.
It is necessary to understand that the experimentation and calculation of two things first will compute the possibility of any event:
Total number of outcomes possible for the experiment
Total number of outcomes for the occurring event
However, this can sound like a time-consuming concept to understand. Still, Class 10 Mathematics chapter 15 Notes will help you learn the chapter’s intricacies and further build your understanding based on the knowledge gained.
We assure you that the prepared notes are carefully tailored by highly qualified mathematics experts from various supreme universities. You will find the much-needed guidance after reading the class 10 maths chapter 15 notes.
Probability 10th Class Notes – Different Kinds of Events
Compound event-
An event is defined as a compound event when it is obtained upon combining two or more elementary events in a random experiment. These events are moreover connected with the occurrence of the random experiment. Hence, compound events are the ones with more than one possible outcome in a random experiment.
Occurrence of an event-
It is when an event is set to occur in a random experiment if any corresponding elementary event is the outcome of the accidental investigation.
Impossible events-
These types of events are considered impossible due to the probability of their occurrence being zero.
Sure event-
A particular event’s occurrence is 1 when it is a specific event.
Class 10 Mathematics Probability Notes – Probability of Cards
A pack of cards consists of a total of 52 cards that are segregated into four suits –
Spades (Black colored)
Hearts (Red colored)
Diamond (Red colored)
Clubs (Black colored)
Each suit contains 13 cards commencing from 1 to 13. However, fewer cards are named differently.
First Card – is called an ‘Ace’ and possesses a symbol of ‘A’ that is followed by a series of numbers starting from 2 to 10.
11th card – is called a ‘Jack’ and is indicated by the symbol’ J.’
The 12th card – is called a ‘Queen’ and is indicated with the symbol ‘Q.’
The 13th card – is called a ‘King’, which has the symbol ‘K’.
Jack, Queen, and King are called the face cards. Therefore, there are 12 face cards in a pack of 52 cards. You can calculate the probability of an event’s occurrence with the help of these numbers.
Since the spades and clubs are considered to be black colored and the hearts along with diamonds to be red-colored, there are a total of 26 black and 26 red cards.
Students who cannot understand and solve probability questions without getting proper information about the events should refer to class 10 maths chapter 15 notes. Becoming familiar with the total outcomes and the potential number of outcomes related to the event in any random experiment will help in scoring good grades on the exam.
You will be more confident in your concepts when you start referring to Class 10 Mathematics Chapter 15 Notes as it is based on the latest NCERT books and covers the ideas for solving CBSE previous year’s questions.
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, the probability of getting seats or heads 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 occasions. 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 to the forefront. Subsequently, you don’t have to invest more time learning a particular concept.
Utilize our quality notes to understand advanced topics better and learn steps to solve exercise questions and last-minute study. Our qualified expert teachers prepare study material that maintains standards per the latest CBSE guidelines. Therefore, studying is more fun with Vedantu as your digital study companion.
Probability Notes Class 10 – Probability of Die
A die has six faces, with every face representing a specific number, which starts from 1 and ends at 6. So, the outcome of the occurrence of any number starting from 1 to 6 is regarded to be equal.
It also means that the probability of occurrence of 1 when a dice is thrown is equal to the likelihood of receiving a 4 on the same. It stands accurate for any other number from 1 to 6. The probability for the occurrence of each event will be ⅙,
Furthermore, you will gain a robust understanding and will be able to analyze the number of outcomes in outcomes upon throwing two or three dice. This will require you to explore the number of possible events in a random trial.
Therefore, if you refer to the CBSE class 10 maths chapter 15 notes, you will find thorough knowledge of the concept of probability. Give a glance through the topics at the last minute via the notes, which will help boost your performance.
Our Probability Chapter Class 10 PDF is an excellent study resource for students that provides pointwise notes on essential topics from an exam perspective. You can access it here.
The Class 10 Mathematics Chapter 15 Notes are an excellent way of revising the integral points of the chapter and grasping a firm understanding of the basics. You can-
- Learn the topics.
- Understand the technique.
- Revise what you have learned.
Fun Facts about Complementary Events
Did you already know that complementary events are named as those events where purely two outcomes can occur, stating whether the event will happen or not? For instance, whether your friend will meet you or not is a complementary event.
It can further be said that complementary events are regarded as the events that occur in the exact opposite manner of whether the probable event will take place or not. A few more examples of complementary events are-
- If it will rain tomorrow or not
- If a student will pass exams or not
- If you will win the lottery or not