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RS Aggarwal Solutions

RS Aggarwal Class 12 Solutions Chapter-29 Probability

RS Aggarwal Class 12 Solutions Chapter-29 Probability

Q: 3. How do you solve a problem on dependent events, such as drawing two balls without replacement?

To solve such problems, you apply the Multiplication Theorem of Probability for dependent events. Let's take an example: A bag has 5 yellow and 7 blue balls. Two balls are drawn one by one without replacement. What is the probability that the first is yellow and the second is blue?Step 1: Find the probability of the first event. The probability of drawing a yellow ball first is P(Y) = 5/12.Step 2: Find the probability of the second event, given the first has occurred. Since the first ball was not replaced, there are now only 11 balls left. The probability of drawing a blue ball second is P(B|Y) = 7/11.Step 3: Apply the multiplication theorem. The required probability is P(Y and B) = P(Y) × P(B|Y).Step 4: Calculate the final answer. (5/12) × (7/11) = 35/132.

Q: 6. What is a common mistake when finding the probability distribution of a random variable?

A common mistake is incorrectly defining the values the random variable (X) can take, or miscalculating the probability for each value. Another frequent error is failing to verify that the sum of all probabilities in the distribution equals exactly 1. For example, when tossing two coins, if X is the number of heads, X can take values 0, 1, or 2. You must calculate P(X=0), P(X=1), and P(X=2) separately and ensure that their sum is 1.

Class 12 RS Aggarwal Chapter-29 Probability Solutions - Free PDF Download

For the students who always want to stay on top of the class, RS Aggarwal solutions class 12 probability is going to be the best help. These solutions help the students have all the preparation that they need to solve some of the more complex problems which are included in the chapter. The students will get to learn more and more about different topics and materials which are covered in the chapter as well. Vedantu has always aimed to assist the students and that is one of the main reasons why it is considered to be one of the top tutoring services available in the country.

Download The Latest RS Aggarwal Class 12 Solutions Chapter 29 Right Now

Chapter 29 of the math textbook for Class 12 deals with probability and students can get to know much more about it from the solutions that are provided to them right here. With the help of these solutions, students can revise the chapter all they need before their examination. Check out the RS Aggarwal Class 12 solutions chapter 29 right now and you won’t regret it for sure. Students will get to know all that they need about changes that occur in a particular event with the help of some very advanced and detailed theorems. With the help of this chapter in RS Aggarwal, they will be able to advance a bit more to understand the meaning of probability and much more. We all know how important it is to have some knowledge about the concept of probability and that is exactly what is provided in the solutions right here.

The whole chapter is divided into several topics and subtopics. Not to mention that there are also a total of about 22 different questions in the 2 exercises which are present. Students will be tackling some important theorems in the chapter such as Bayes Theorem, Multiplication Theorem of Probability, Partition of Sample Space, the Theorem of Total Probability, and much more. Check the solutions for RS Aggarwal Class 12 Math Chapter 29 right now. All of these pieces of information are surely going to be a huge help in the studies for sure. One of the most important things to keep in mind about the questions is that these are created to make sure that the students get enough practice for their final exams. So, the questions are definitely in the format of the CBSE standards. For those who need to ensure that they are always on top of the class, there is simply not a single speck of doubt about the fact that having some help from these solutions will not be a bad idea for sure.

Apart from their final exams, some students also tend to have some difficulty when they are preparing for their important entrance exams. Probability has a very important hold on these exams and hence the preparation for competitive exams becomes a lot easier when they are practicing from the solutions for RS Aggarwal Class 12 chapter 29. Having some sort of help from these solutions along with some robust practice will ensure that these students get to have the desired marks that they want. All of the solutions for the exercise have been covered based on the topics which makes it pretty easy to understand as well. Some simpler events are easy to calculate and there are some tougher questions as well which can be tackled after a lot of practice. So, the students are accustomed to pretty much everything right here.

Prepare With The Best Solutions For RS Aggarwal Class 12 Chapter 29 Math

There is simply no doubt when we say that RS Aggarwal Solutions Class 12 probability will be a game-changer for the students who want to stay ahead of their class and score some good marks in the exams as well. You will also be able to manage your time well with thorough practice with these solutions. All of the solutions have been created by the experts and hence are provided in a very detailed and simple manner that makes it very easy to understand. So, taking the help of the RS Aggarwal Class 12 solutions chapter 29 might just be the best thing for the students preparing for their examinations.

Important Topics from the RS Aggarwal Class 12 Chapter-29 Probability

The RS Aggarwal Class 12 Chapter 29 teaches you about Probability and the concepts related to it. Here is a brief introduction of the topics you will be learning in this chapter:

Conditional Probability - It refers to the occurrence of one event based on the occurrence of one or more previous events.

For example, A and B are two events of the same sample set of an experiment. The conditional probability of A given that B has already happened will be:

P(E|F) = P(E ∩ F) ÷ P(F)

Multiplication Theorem - According to this theorem, the probability of two events, say A and B, occurring simultaneously will be equal to the product of the probability of B and the conditional probability that A is occurring when B has already occurred.

If A and B are dependent events, the probability of both of them occurring simultaneously will be: P(A ∩ B) = P(B) × P(A|B)

However, if the events, A and B, are independent, the probability of their simultaneous occurrence will be: P(A ∩ B) = P(A) × P(B)

Independent Events: Any event that occurs without any interference by another event is known as an independent event. Two events are independent when the occurrence of one does not affect the occurrence of the other.

For Example, the event A will be independent of the event B if the probability of A is equal to the conditional probability of A i.e. P(A) = P(A | B)

Benefits of RS Aggarwal Class 12 Solutions Chapter-29 Probability

The RS Aggarwal Class 12 Solutions Chapter-29 Probability comes with many benefits. It provides you with step-by-step solutions to a variety of questions based on the same pattern as your board exam. It helps you revise the concepts of probability and practice the important questions related to them. The RS Aggarwal Class 12 Solutions Chapter-29 Probability will also show you how you can present the mathematical equations in your solutions to gain maximum marks. Furthermore, it gives you an overview of the concepts such as conditional probability, independent events, etc., that will be helpful in further studies.

FAQs on RS Aggarwal Class 12 Solutions Chapter-29 Probability

1. What are the major topics covered in the RS Aggarwal Solutions for Class 12 Maths Chapter 29, Probability?

The solutions for this chapter provide detailed, step-by-step methods for key concepts aligned with the CBSE 2025–26 syllabus. You will find extensive practice on:

Conditional Probability: Calculating the probability of an event when another event has already occurred.
Multiplication Theorem on Probability: Finding the probability of the intersection of two or more events.
Independent Events: Solving problems where the occurrence of one event does not affect the other.
Bayes' Theorem: Applying reverse probability to determine the probability of an earlier event given a later event has occurred.
Probability Distribution of a Random Variable: Tabulating the probabilities for each possible outcome of a random variable.

2. How do the RS Aggarwal solutions for Class 12 Probability improve board exam preparation?

These solutions are designed to build problem-solving skills for the board exams. They help by:

Providing Variety: Offering a wide range of questions beyond the NCERT textbook, which prepares you for different problem formats.
Clarifying Methods: Presenting clear, step-by-step answers that help you understand the correct method to use for each type of question.
Reinforcing Concepts: By working through numerous solved examples, you can solidify your understanding of complex topics like Bayes' theorem and conditional probability.
Building Confidence: Successfully solving the variety of problems in RS Aggarwal boosts your confidence for tackling any question in the final exam.

3. How do you solve a problem on dependent events, such as drawing two balls without replacement?

To solve such problems, you apply the Multiplication Theorem of Probability for dependent events. Let's take an example: A bag has 5 yellow and 7 blue balls. Two balls are drawn one by one without replacement. What is the probability that the first is yellow and the second is blue?

Step 1: Find the probability of the first event. The probability of drawing a yellow ball first is P(Y) = 5/12.
Step 2: Find the probability of the second event, given the first has occurred. Since the first ball was not replaced, there are now only 11 balls left. The probability of drawing a blue ball second is P(B|Y) = 7/11.
Step 3: Apply the multiplication theorem. The required probability is P(Y and B) = P(Y) × P(B|Y).
Step 4: Calculate the final answer. (5/12) × (7/11) = 35/132.

4. What is the difference in approach between solving a problem using the theorem of total probability and Bayes' theorem?

Both theorems are crucial, but they answer different types of questions. The Theorem of Total Probability is used to find the probability of an event by considering all possible scenarios that could lead to it. It calculates a 'forward' probability, like finding the overall chance of selecting a defective item from a factory with multiple machines. In contrast, Bayes' Theorem finds a 'reverse' conditional probability. If you already know an item is defective, Bayes' theorem helps calculate the probability it came from a specific machine.

5. Why is it a bad idea to skip RS Aggarwal's Chapter 29 on Probability for the Class 12 exams?

Skipping this chapter is not recommended. Probability is a high-weightage unit in the CBSE Class 12 Maths board exam, typically accounting for around 8 marks. The questions in RS Aggarwal cover all essential concepts and problem variations that are frequently asked. Mastering this chapter through these solutions ensures you are prepared for a significant portion of the exam paper and do not lose crucial marks.

6. What is a common mistake when finding the probability distribution of a random variable?

A common mistake is incorrectly defining the values the random variable (X) can take, or miscalculating the probability for each value. Another frequent error is failing to verify that the sum of all probabilities in the distribution equals exactly 1. For example, when tossing two coins, if X is the number of heads, X can take values 0, 1, or 2. You must calculate P(X=0), P(X=1), and P(X=2) separately and ensure that their sum is 1.

7. How do the questions in RS Aggarwal's Probability chapter differ from the NCERT textbook?

While NCERT provides the fundamental concepts and standard problems, RS Aggarwal expands on them significantly. The key difference lies in the volume and variety of questions. RS Aggarwal includes a larger number of practice problems, covering more complex and varied scenarios for each topic like conditional probability and Bayes' theorem. This makes it an excellent supplementary resource for students aiming to achieve a higher score by mastering a wider range of applications.