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Complete Maths Probability and Statistics JEE Main Notes for 2025 Preparation

Q: 8. How To learn using JEE Main 2025 Statistics and Probability Notes?

Understand the fundamental concepts, definitions, and laws.Practice solving a variety of problems to grasp different scenarios.Focus on application-based questions to connect theory with practical situations.Create a summary sheet with key formulas and concepts.Analyse your mistakes and learn from them.

JEE Main

Revision Notes

Maths

Statistics And Probability

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Study Smart with JEE Main - Statistics and Probability Notes and Important Topics

The Statistics and Probability, a crucial chapter for the JEE Main Exam, covers the mathematical study of data analysis, probability theory, and statistical methods. Get ready for your JEE Main exam by getting hold of important Statistics and Probability JEE Main Maths Notes. Our expert teachers create these notes to make tough concepts easy, highlight important stuff, and cover important topics. You can get them for FREE from our website. These notes give you all the important info you need in a simpler way, helping you study better. You'll understand the subjects well and be well-prepared for the exam after reviewing these notes. Use these helpful resources to do great in JEE Main.

Table of Content

1. Year wise Weightage of Questions: JEE Main Statistics and Probability

2. Important Formulas for Sequences and Series

2.1

Statistics Formulas

2.2

Probability Formulas

3. Why Notes of Statistics and Probability Important for JEE Main 2025?

4. Explore Further: Supplementary Resources for JEE Main 2025 Statistics and Probability

5. Access the Supplementary Resources for JEE Main 2025 here:

6. Maths Notes for JEE Main 2025 Chapters: Links Available

7. Download Subject-wise Notes for JEE Main

8. Important Study Materials Links for JEE Exams

FAQs

Year wise Weightage of Questions: JEE Main Statistics and Probability

This is a crucial chapter for JEE Main Exams, and you can expect at least two questions from it. Check out how many questions were asked from the Statistics and Probability chapter in the last five years of JEE Main exams.

S. No	Year	Average No. of Questions Asked	Marks per Question	Total Marks
1	2024	2	4	8
2	2023	2	4	8
3	2022	2	4	8
4	2021	2	4	8
5	2020	2	4	8

The master teachers of Vedantu worked hard to ensure the Statistics and Probability notes perfectly matched the JEE Main syllabus. So, gear up to succeed – grab your Statistics and Probability Notes now and shine in JEE Main 2025!

Top Concepts to Study in Statistics and Probability for JEE Main 2025

Here, you will look at the main topics you should review in Statistics and Probability. these crucial topics can truly improve your preparation. Good at them will give you a big advantage in the upcoming test. So, let's discuss the essential topics you need to consider for success in JEE Main 2025.

Descriptive Statistics
Probability Basics
Probability Distributions
Conditional Probability
Random Variables
Probability Functions
Correlation and Regression
Sampling and Estimation
Hypothesis Testing
Counting and Permutations
Probability Applications
Expected Values and Variance

Important Formulas for Sequences and Series

Statistics Formulas

Mean (Average):

For a set of n values $x_1, x_2, \dots, x_n$:

$\text{Mean} = \dfrac{x_1 + x_2 + \dots + x_n}{n}$

Median:

For an odd number of data points: Median=Middle value when data is arranged in order.
For an even number of data points: Median = $\dfrac{\text{Sum of two middle values}}{2}$

Mode:

The value that appears most frequently in a data set.

Variance ($\sigma^2$):

For a population: $\sigma^2 = \dfrac{1}{n} \sum_{i=1}^{n} (x_i - \mu)^2$
For a sample: $s^2 = \dfrac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2$

Standard Deviation ($\sigma$ or s):

Standard deviation is the square root of variance: $\sigma = \sqrt{\sigma^2} \quad \text{or} \quad s = \sqrt{s^2}$

Coefficient of Variation (CV):

Measures the relative variability of data: $\text{CV} = \dfrac{\sigma}{\mu} \times 100$

Probability Formulas

Basic Probability Formula:

For an event A: P(A)=Number of favorable outcomesTotal number of outcomesP(A) = $\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Addition Rule (for mutually exclusive events):

For two events A and B: P(A∪B)=P(A)+P(B)$

Addition Rule (for non-mutually exclusive events):

For two events A and B: P(A∪B)=P(A)+P(B)−P(A∩B)

Multiplication Rule (for independent events):

For two independent events A and B: P(A∩B)=P(A)×P(B)

Conditional Probability:

For events A and B: P(A | B) = $\dfrac{P(A \cap B)}{P(B)}$ (Probability of A given B)

Bayes’ Theorem:

For events A and B: $P(A | B) = \dfrac{P(B | A) P(A)}{P(B)}$

Binomial Probability:

For n trials and probability of success p: $P(X = k) = \binom{n}{k} p^k (1-p)^{n-k}$ Where $\binom{n}{k}$ is the binomial coefficient.

Mean of Binomial Distribution:

The expected value for binomial distribution: $\mu = np$

Variance of Binomial Distribution:

The variance for binomial distribution: $\sigma^2 = np(1 - p)$

Normal Distribution:

The probability density function for a normal distribution is: $f(x) = \dfrac{1}{\sigma \sqrt{2 \pi}} e^{-\dfrac{(x - \mu)^2}{2\sigma^2}}$ Where $\mu$ is the mean and $\sigma$ is the standard deviation.

These formulas and rules are fundamental for probability calculations in various scenarios.

Why Notes of Statistics and Probability Important for JEE Main 2025?

As you tread the path toward JEE Main 2025, the significance of "Statistics and Probability" notes becomes increasingly evident. This chapter, poised at the intersection of mathematics and real-world applications, offers a unique toolkit that not only elevates your exam performance but also nurtures your analytical reasoning and decision-making skills. Let’s check out few features of the chapter.

Practical Insight:

Statistics and Probability notes usher you into the realm of data analysis, enabling you to make informed decisions and predictions based on empirical evidence.

Real-world Relevance:

This chapter bridges mathematics with real-life scenarios, as probability and statistics are woven into various fields such as economics, science, and social sciences.

Statistical Analysis:

Notes highlights data collection, organization, representation, and interpretation, vital skills in scientific research and decision-making processes.

Probability Fundamentals:

Understanding the principles of probability grants you the ability to quantify uncertainty, essential for predicting outcomes in various scenarios.

Data Interpretation:

Proficiency in statistics empowers you to analyse and interpret data sets, a skill tested not only in exams but also in various professions.

Probability Models:

Notes introduce you to probability distributions, helping you model and analyse random events and their outcomes.

Risk Assessment:

With probability concepts, you gain the competence to assess risks, a crucial skill in fields such as finance and engineering.

Combinatorics and Permutations:

Solving permutations and combinations equips you to solve diverse counting problems.

Decision-making Skills:

By delving into statistics, you cultivate the art of making decisions based on evidence, a trait indispensable in academic and professional spheres.

Critical Analysis:

This chapter encourages critical analysis of data, fostering a discerning mind that evaluates information with depth and precision.

Engineering and Science Applications:

Statistics and Probability are integral in engineering, physics, and medical research, enhancing their real-world application.

Foundation for Further Studies:

Proficiency in this chapter forms a cornerstone for advanced studies in statistics, data science, and related fields.

Holistic Growth:

While preparing for JEE Main, Statistics and Probability notes nurture logical thinking, data literacy, and intellectual maturity.

Problem-solving Aptitude:

Beyond exams, the skills gained empower you to approach challenges methodically, utilizing statistical tools to unravel complexities.

In your pursuit of success in JEE Main 2025, Statistics and Probability notes offer more than just exam preparation. They shape you into a thinker equipped with the ability to decipher data-driven puzzles, make calculated decisions, and appreciate the vital role mathematics plays in shaping our world. As you engage with this chapter, you're not only preparing for an exam, but fostering skills that will reverberate throughout your academic journey and future endeavours.

Strategic Approach: Maximizing Learning with Formulas and Revision Notes

When you want to learn effectively, you can use a smart strategy by combining formulas and revision notes. These two things work together nicely. Formulas are like short explanations of important ideas. Using them with detailed revision notes gives you a complete way to learn. Revision notes give you a strong base, and formulas help you understand better and solve problems. This mix makes hard things easier and helps you remember better. By using this strategy, you can improve how well you understand and do well in your studies.

Download the JEE Main Maths Formulas by Vedantu for FREE. Combine it with JEE Main Notes, and you can see the good changes in your scores.

Effective Tips for JEE Mains Preparation on Statistics and Probability

Ensure you have a solid grasp of core concepts like mean, median, mode, variance, and standard deviation. These are essential building blocks for solving problems in both statistics and probability.
Memorise the important formulas, especially for probability, permutations, combinations, and binomial distribution. Familiarity with these formulas will help you solve problems quickly and efficiently.
Solve as many practice problems as you can. Work on problems of different difficulty levels to improve your problem-solving skills. The more variety you tackle, the better you'll become at identifying the right approach.
Spend extra time understanding conditional probability, as it is a frequently tested topic in JEE. Practice applying the conditional probability formula in various scenarios to become more confident.
Review important topics and formulas frequently. Regular revision helps reinforce concepts and ensures you don’t forget crucial details leading up to the exam.
Go through previous year’s JEE Main and Advanced papers to identify common types of problems and patterns. This helps you understand the exam’s expectations and prepares you for similar questions.

Explore Further: Supplementary Resources for JEE Main 2025 Statistics and Probability

Looking to enhance your JEE Main 2025 Statistics and Probability preparation? Explore these Important materials:

Practice Papers: Enhance your abilities through focused practice.
Mock Tests: Replicate exam scenarios for increased confidence.
Sample Papers: Get acquainted with question formats.
Previous Year Question Papers (PYQPs): Understand exam patterns.

Use these tools to improve comprehension and test-taking skills, boosting your JEE Main 2025 performance!

Access the Supplementary Resources for JEE Main 2025 here:

S. No	Other Important Links for JEE Main 2025
1	JEE Main Statistics and Probability Practice Papers 2025
2	JEE Main Statistics Mock Test 2025
3	JEE Main Probability Mock Test 2025
4	JEE Main Statistics and Probability Important Questions 2025

Enhance your Results with Vedantu’s JEE Main Notes

As you work hard to do well in JEE Main 2025, think of Probability And Statistics JEE Main Notes as your helpful friend. They simplify hard things, show what's important, and let you practice, which improves your study. Vedantu's JEE Main notes help you, and you'll understand things, solve problems without fear, and do well in the exam. Get the Statistics and Probability Revision Notes for FREE to get better and succeed in JEE Main 2025.

Maths Notes for JEE Main 2025 Chapters: Links Available

Make your JEE Main Maths studying for 2025 even better using our notes organized by chapter. Find the links in the table below for easy access.

S. No	JEE Main 2025: Chapterwise Links to Maths Notes
1	Unit 1 Sets, Relations and Functions JEE Notes
2	Unit 2 Complex Numbers and Quadratic Equations JEE Notes
3	Unit 3 Matrices and Determinants JEE Notes
4	Unit 4 Permutations and Combinations JEE Notes
5	Unit 5 Binomial Theorem and Its Simple Applications JEE Notes
6	Unit 6 Sequence and Series JEE Notes
7	Unit 7 Limit, Continuity and Differentiability JEE Notes
8	Unit 8 Integral Calculus JEE Notes
9	Unit 9 Differential Equations JEE Notes
10	Unit 10 Co-ordinate Geometry JEE Notes
11	Unit 11 Three-Dimensional Geometry JEE Notes
12	Unit 12 Vector Algebra JEE Notes
13	Unit 14 Trigonometry JEE Notes

Download Subject-wise Notes for JEE Main

Get the links to download the subject-wise JEE Main Notes PDF for FREE from the table below.

S. No	Subject	Notes PDF
1	Physics	JEE Main Physics Notes
2	Chemistry	JEE Main Chemistry Notes

Important Study Materials Links for JEE Exams

S. No	Essential Study Material Links for JEE
1	JEE Advanced Notes
2	JEE Main Important Question
3	JEE Advanced Important Question
4	JEE Main Question Paper
5	JEE Advanced Question Paper
6	JEE Main Sample Paper
7	JEE Advanced Sample Paper
8	JEE Advanced Syllabus
9	JEE Main Mock Test Series
10	JEE Advanced Mock Test Series
11	JEE Preparation Tips
12	JEE Main Formulas
13	JEE Advanced Formulas
14	JEE Main Difference Between
15	JEE Advanced Difference Between
16	JEE Main Topic
17	JEE Main Question and Answers
18	JEE Advanced Question and Answers

FAQs on Complete Maths Probability and Statistics JEE Main Notes for 2025 Preparation

1. What are the most important topics included in Statistics and Probability Notes for JEE Main 2025?

Important topics in JEE Main 2025 Statistics and Probability Notes include:

Measures of central tendency and dispersion.
Probability concepts and laws.
Probability distributions (binomial, normal).
Permutations and combinations.
Random variables and their distributions.
Sampling and sampling distributions.

2. What is the weightage of Statistics and Probability Notes for JEE Main 2025?

The weightage of Statistics and Probability Notes in JEE Main 2025 is typically around 10-12% of the overall mathematics section, making it a significant part of the exam.

3. Which is the easiest topic of JEE Main 2025 Statistics and Probability Notes?

The easiest topic can vary based on individual understanding, but many students find measures of central tendency (mean, median, mode) relatively straightforward.

4. What are the Statistics and Probability in the context of JEE Main 2025?

In the context of JEE Main 2025, Statistics and Probability refer to the mathematical study of data analysis, uncertainty quantification, and predicting outcomes based on probability principles.

5. How can I apply the Statistics and Probability to solve JEE Main problems?

To Apply statistics and Probability to solve JEE Main problems:

Understand the problem context and data given.
Apply relevant probability concepts and laws.
Perform calculations for measures of central tendency or probability distributions.
Interpret results in the context of the problem.

6. Are there any common mistakes students make in Statistics and Probability problems?

Common mistakes students make in Statistics and Probability problems include misinterpreting data, misunderstanding probability laws, and miscalculating probabilities or statistics.

7. What are the expected difficulty level of JEE Main Statistics and Probability questions?

The difficulty level of Statistics and Probability questions in JEE Main can vary from moderate to challenging. They may involve intricate calculations or require a deep understanding of probability concepts.

8. How To learn using JEE Main 2025 Statistics and Probability Notes?

Understand the fundamental concepts, definitions, and laws.
Practice solving a variety of problems to grasp different scenarios.
Focus on application-based questions to connect theory with practical situations.
Create a summary sheet with key formulas and concepts.
Analyse your mistakes and learn from them.

9. Where can I find the best resources for Probability and Statistics for JEE Main 2025?

You can find comprehensive resources like Probability and Statistics JEE Main Notes on Vedantu, where you can download JEE Probability and Statistics Notes PDF for free. These notes offer a clear explanation of key topics and essential formulas.

10. How can JEE Main Probability and Statistics Notes PDF help in exam preparation?

JEE Main Probability and Statistics Notes PDF serve as a condensed version of all critical topics. They simplify complex concepts, provide important formulas, and help you revise effectively, saving time during the exam preparation phase.

11. What is the difference between Probability and Statistics JEE Notes and other study materials?

Probability and Statistics JEE Notes are specifically curated to focus on topics relevant to the JEE Main syllabus, offering clear explanations, examples, and step-by-step solutions. These notes are more targeted towards JEE Main exam patterns and help in solving problems efficiently.

12. How often should I refer to JEE Main Probability and Statistics Notes for effective preparation?

It’s ideal to refer to JEE Main Probability and Statistics Notes regularly during your revision phase. Set aside time each week to go over these notes, solve problems, and focus on areas where you need improvement.

13. Are the JEE Main Probability and Statistics Notes suitable for last-minute revision?

Yes, JEE Main Probability and Statistics Notes are perfect for last-minute revision as they highlight key concepts and formulas in a concise manner. Reviewing these notes before the exam will help reinforce your understanding and improve your speed.

14. Can I rely only on JEE Probability and Statistics Notes for my preparation?

While JEE Probability and Statistics Notes are a great resource, it is important to complement them with practice from previous year papers, mock tests, and a deep understanding of the theory behind each concept. Solving a variety of problems will enhance your problem-solving ability.

15. How do Probability And Statistics JEE Notes PDF help in understanding probability distributions?

JEE Probability and Statistics Notes provide clear explanations and examples of different probability distributions, such as binomial and normal distributions. These notes include problems that help you apply the concepts and solve distribution-related questions.

16. What are the key topics to focus on in Probability and Statistics JEE Main Notes for 2025 preparation?

Focus on fundamental topics such as probability laws, permutations and combinations, probability distributions (binomial, normal), mean, median, mode, variance, and the concepts of random variables. These are key topics covered in Probability and Statistics JEE Notes.

17. How can I improve my problem-solving skills using JEE Probability and Statistics Notes?

Practice regularly using problems from JEE Probability and Statistics Notes. By solving a wide range of problems, you will improve your application of probability and statistical concepts, allowing you to tackle even the most challenging questions in JEE Main.

18. What should I do if I don’t understand certain concepts in Probability and Statistics JEE Notes PDF?

If you find certain concepts unclear, refer to additional resources like video lectures, textbooks, or seek help from a teacher. JEE Probability and Statistics Notes PDF provide a solid foundation, but sometimes further explanation might be needed for deeper understanding.