# RS Aggarwal Class 12 Chapter 30 Solutions (Baye’s Theorem and Its Applications)

RS Aggarwal Solutions for Class 12 Chapter 30 Bayes’ Theorem and Its Applications are given keeping in mind the advancement of concepts of probability as you progress. In RS Aggarwal Solutions, You will be astonished to know the tricks you can play to calculate the probability of almost any possibly occurring event. Bayes’ Theorem is based on the logic of conditional probability. You will learn to find the probability of occurrence of a given event taking into consideration many more conditions that can be influencing the event. This topic is of vital importance in medical science, artificial intelligence and many more areas.

This chapter consists of 1 exercise comprising 18 questions. The questions are very important from the exam point of view as these questions belong to the recurring category of questions in the question papers. The answers are very detailed as this is a very tricky and conceptual topic. Bayes’ Theorem will aid you in higher studies and research work if you aspire to become a scientist. It is advised that you supplement your NCERT book with these answers of RS Aggarwal questions Chapter 30.

We, at Instasolv, will make sure you get complete clarity on this chapter. Instasolv experts are aware of the importance of this chapter for the board exam as well as the entrance exam of eminent technical institutes, therefore they have created the solution in a fashion that will be compatible to your level of understanding about the topic. After practising these solutions, you will have a better approach to the questions in your exams.

## Summary of Topics in RS Aggarwal Solutions for Class 12 Chapter 30 – Bayes’ Theorem and Its Applications

**Introduction to Bayes’ Theorem**

Bayes’ Theorem explains and defines a way to calculate the probability of occurrence of a given event which is influenced by other conditions. Therefore, it is also often termed as a kind of conditional probability. This can be explained with the help of an example, suppose you need to find the probability of drawing out a yellow ball from the third bag among three separate bags of balls, which contain balls of three different colours, that is, yellow, red and green. In such a situation, the probability of the occurrence of your desired event is calculated taking into consideration these other events. Such a case is known as conditional probability.

**Statement of the Theorem:**

If there are a set of events given as E1, E2, …, En which have an association to a given sample space denoted as S, and if all these events E1, E2, …, En have a non-zero probability of occurrence, hence forming a partition of the given sample space S. Assuming any event A associated with the sample space S, then as per Bayes’ Theorem

k=1, 2, 3,…, n

**Proof:**

Using the formula of conditional probability which is given as

P(Ei/A)=P(Ei).P(A|Ei)

And the rule of multiplication in probability is given as,

Also, by the Total Probability Theorem,

Hence, by putting the values of P(A) and P(EiA) in the conditional probability formula, you get the Bayes’ Theorem as

**Applications:**

You can employ the Bayes Conditional Probability Theorem in the following two cases amongst its various applications:

- It can be used to calculate the probability of the occurrence of some future events.
- You can calculate the posterior probability of the desired event with the help of earlier probability of some events.

## Key Highlight of Bayes’ Theorem and Its Applications:

- Bayes’ Theorem is mathematically given as

- It is used to calculate the probability of the occurrence of some future events.
- It is used to calculate the posterior probability of the desired event with the help of earlier probability of some events.

## Discussion of Exercise Questions of RS Aggarwal Solutions for Class 12 Chapter 30 – Bayes’ Theorem and Its Applications

- The exercise solutions in these chapters comprise 18 long answer type questions.
- These questions are mostly situational based and have practical applications.
- By solving the questions of RS Aggarwal Chapter 30, you will learn to approach the questions related to conditional probability with the correct formula.
- These questions will help you practice the tricks to identify the application of Bayes’ Theorem easily.
- You can rely on these questions for comprehensive coverage of all possible concepts in this Chapter.

## Benefits of RS Aggarwal Solutions for Class 12 Maths Chapter 30 by Instasolv

The solutions are prepared by maths experts at Instasolv to make sure you get clarity in this chapter. Practising the RS Aggarwal Solutions Class 12 Solutions for Chapter 30 will help you achieve good marks in maths and will enhance your overall score. We have designed step by step solutions to help you solve all your queries related to the chapter.