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# NCERT Solutions for Class 12 Maths Chapter 13 Exercise 13.3 Probability - PDF Download

NCERT solutions for class 12 maths chapter 13 exercise 13.3 Probability talks about the concepts of bayes’ theorem, partition of a sample space and theorem of total probability. Questions included in ex 13.3 are highly focused on a deep understanding of these topics and concepts. eSaral’s subject experts of mathematics have prepared all these solutions in an easy and precise language for strong foundation of core concepts to achieve higher marks in board exams.

With the help of interactive visuals in NCERT solutions for ex 13.3 class 12 maths chapter 13, students can grasp a thorough understanding  of these topics. There are a total of 14 sums in ex 13.3 class 12 maths solutions that provide a straightforward approach to find the partition of a sample space and theorem of total probability. You can use the NCERT solutions for ex 13.3 for learning the concepts of bayes’ theorem and solving the questions error-free.

NCERT solutions for ex 13.3 class 12 maths are also made available in PDF format at eSaral. You can download the free PDF from our official website or you can practice all the questions online at eSaral. Here, we have provided the link below to download the free PDF.

## Topics Covered in Exercise 13.3 Class 12 Mathematics Questions

Class 12 maths chapter 13 exercise 13.3 NCERT solutions is based on an important theorem of bayes’s theorem and partition of a sample space, theorem of total probability.

 1 Bayes' Theorem Partition of a sample space Theorem of total probability
1. Bayes' Theorem

Famous mathematician John Bayes' solved the problem of finding reverse probability by using conditional probability. The formula developed by him is known as ‘Bayes theorem’.

Bayes' theorem - If E1 , E2 , ..., En are events which constitute a partition of sample space S, i.e. E1 , E2 , ..., En are pairwise disjoint and $\mathrm{E}_1 \cup \mathrm{E}_2 \cup \ldots \cup \mathrm{E}_n=\mathrm{S}$ and A be any event with nonzero probability, then

$\mathrm{P}\left(\mathrm{E}_i \mid \mathrm{A}\right)=\frac{\mathrm{P}\left(\mathrm{E}_{\mathrm{i}}\right) \mathrm{P}\left(\mathrm{A} \mid \mathrm{E}_{\mathrm{i}}\right)}{\sum_{j=1}^n \mathrm{P}\left(\mathrm{E}_j\right) \mathrm{P}\left(\mathrm{A} \mid \mathrm{E}_j\right)}$

• Partition of a sample space

A set of events E1 , E2 , ..., En is said to represent a partition of the sample space S if

1. $\mathrm{E}_i \cap \mathrm{E}_j=\phi, i \neq j, i, j=1,2,3, \ldots, n$

2. $\mathrm{E}_1 \cup \mathrm{E}_2 \cup \ldots \cup \mathrm{E}_n=\mathrm{S}$

3. $\mathrm{P}\left(\mathrm{E}_i\right)>0$ for all $i=1,2, \ldots, n$.

In other words, the events E1 , E2 , ..., En represent a partition of the sample space S if they are pairwise disjoint, exhaustive and have nonzero probabilities.

• Theorem of total probability

Let {E1 , E2 , ...,En ) be a partition of a sample space and suppose that each of E1 , E2 , ..., En has nonzero probability. Let A be any event associated with S, then

$\mathrm{P}(\mathrm{A})=\mathrm{P}\left(\mathrm{E}_1\right) \mathrm{P}\left(\mathrm{AlE}_1\right)+\mathrm{P}\left(\mathrm{E}_2\right) \mathrm{P}\left(\mathrm{AlE}_2\right)+\ldots+\mathrm{P}\left(\mathrm{E}_n\right) \mathrm{P}\left(\mathrm{AlE}_n\right)$

## Tips for Solving Exercise 13.3 Class 12 Chapter 13 Probability

As ex 13.3 class 12 maths ch 13 describes the theorem of total probability and partition of a sample space, you need to have a clear understanding of these concepts to solve questions of ex 13.3 class 12 maths. Our subject experts of eSaral have mentioned here some of the useful tips that can be followed by you.

1. Students need to have a strong hold on the theorem and its applications to solve sums with ease.

2. There are examples before exercise that you should solve for better understanding of questions.

3. Students are also advised to solve all the questions on their own to comprehend which topic needs more attention to improve. By doing this, they can strategize their learning.

## Importance of Solving Ex 13.3 Class 12 Maths Chapter 13 Probability

You will find various benefits of solving questions in ex 13.3 class 12 maths chapter 13 Probability. You can check below some of the benefits provided by the expert faculty of eSaral.

1. NCERT solutions for ex 13.3 class 12 maths chapter 13 are explained by subject experts of eSaral. You can use these solutions while solving questions when you get stuck or confused.

2. Ex 13.3 class 12 maths is solved in a step by step manner that provide you conceptual knowledge of each topics

3. Practicing questions in NCERT solutions will provide you accurate answers for all the sums that help you score good marks in exams.

4. Practicing questions with NCERT solutions can improve your problem-solving skills.