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

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.
   

Frequently Asked Questions

Question 1. What do you understand by Bayes's theorem?

Answer 1. Bayes’ theorem is a mathematical theorem that is used to get the conditional probability of an event. Conditional probability will occur in future. It is calculated based on the outcome of an event which has occurred previously. 

Question 2. When should I use the Bayes’ theorem?

Answer 2. Bayes’ theorem can be used when the conditional probability of an event is given. This is used to find the reverse probability of an event.