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Subject specialists have created NCERT Exemplar Solutions for Class 12 Maths Chapter 13 Probability, which includes thorough solutions for reference. All of the questions from the textbook’s exercises are answered here. Students can use these answers to help them prepare for their exams. The NCERT Exemplar Solutions for Class 12 provide useful solutions for improving conceptual knowledge and preparing for **JEE**.

The solutions are carefully solved using student-friendly terms while still adhering to the norms that must be followed when solving NCERT Exemplar Solutions for Class12. Practicing these answers can be incredibly advantageous not only in terms of exams but also in terms of helping Class 12pupils perform well in upcoming competitive exams.

The approaches for answering have been given special consideration to stay on target while not deviating from the intended answer. Because time is so important in exams, excellent time management when answering questions is essential for getting the best results.

Following are the topics and subtopics explained in Class 12 Chapter 13- Probability of **NCERT Exemplar Solutions**:

13.1 Introduction

13.2 Conditional Probability

13.2.1 Properties of conditional probability

13.3 Multiplication Theorem on Probability

13.4 Independent Events

13.5 Bayes’ Theorem

13.5.1 Partition of a sample space

13.5.2 Theorem of total probability

13.6 Random Variables and its Probability Distributions

13.6.1 Probability distribution of a random variable

13.6.2 Mean of a random variable

13.6.3 Variance of a random variable

13.7 Bernoulli Trials and Binomial Distribution

13.7.1 Bernoulli trials

13.7.2 Binomial distribution

The chapter Probability is part of a larger unit, Unit Six- Probability, which is worth 8 out of a total of 80 points. This chapter includes two exercises as well as a miscellaneous activity to assist students fully grasp the basics of probability.

Following are the concepts discussed in Chapter 13 of NCERT Exemplar Solutions for Class 12 Maths:

- 0 ≤ P (E|F) ≤ 1, P (E′|F) = 1 – P (E|F)P ((E ∪ F)|G) = P (E|G) + P (F|G) – P ((E ∩ F)|G)
- P (E ∩ F) = P (E) P (F|E), P (E) ≠ 0P (E ∩ F) = P (F) P (E|F), P (F) ≠ 0
- If E and F are independent, then P (E ∩ F) = P (E) P (F)P (E|F) = P (E), P (F) ≠ 0P (F|E) = P (F), P(E) ≠ 0
- Total probability theorem
- Bayes’ theorem
- A random variable is a real-valued function whose domain is a random experiment’s sample space.
- Var (X) = E (X2) – [E(X)]2
- If the below conditions are satisfied, then the Trials of a random experiment are called Bernoulli trials :
- A set number of trials should be available.
- The trials should be self-contained.
- There are only two possible outcomes in each trial: success or failure.
- In each trial, the chances of success are the same.

To learn more about concepts linked to Probability, read Chapter 13 of the NCERT textbook for Maths. NCERT Exemplar Solutions for Class 12 Maths Chapter 13 can be used as a quick reference to help students understand complicated concepts.

**Key Features of NCERT Exemplar Solutions for Class 12 Maths Chapter 13- Probability**

Conditional probability, the multiplication theorem on probability, independent events, total probability, Bayes’ theorem, Random variable and its probability distribution, mean and variance of a random variable are all covered in the chapter “Probability” of Class 12 NCERT Exemplar Solutions.

**Frequently Asked Questions**

##### Where can I get NCERT Exemplar Solutions for Class 12 Maths Chapter 12 online?

INFINITY LEARN has the NCERT Exemplar Solutions for Class 12 Maths Chapter 12 available for download. Subject specialists curate the solutions to all of the problems so that students have the best reference material to rely on. You can download chapter-by-chapter or exercise-by-exercise solutions to acquire a better understanding of the problem-solving approaches used to solve textbook issues.

##### Explain the concept of conditional probability in Chapter 13 of NCERT Exemplar Solutions for Class 12 Maths.

The probability of events that occur in connection to one or more events is explained by conditional probability. If A and B are two events in the same sample space in a random experiment, the conditional probability of event A will be the same as the conditional probability of event B.

##### Why NCERT Exemplar Solutions for Class 12 Maths Chapter 13 is beneficial for the students to score well in the second term exams?

The specialists at INFINITY LEARN deliver NCERT Exemplar Solutions for Class 12 Maths Chapter 13 that are tailored to the students' understanding skills. Students can obtain the solution module PDF from infinity learn according on their needs. All of the major exam ideas are taught in plain English to assist students ace the term – II exam with confidence. The solutions to all of the problems in the NCERT textbook assist students in double-checking their answers and analysing their weak spots.

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