JEE Main Statistics and Probability Practice Paper with Solutions and Answer Key

JEE Main Maths is one of the most important subjects for engineering aspirants, and it requires a thorough understanding of the fundamental concepts and principles. Statistics and Probability is a crucial topics in JEE Main Maths, and mastering this topic can help students score well in the exam. One of the best ways to prepare for JEE Main Maths is by solving practice papers on Statistics and Probability. In this article, we will discuss the importance of JEE practice paper for Statistics and Probability, Maths and how they can help students improve their problem-solving skills and test their knowledge of the concepts. These practice papers are available in various formats, including online and offline form.

Topics of JEE Main Maths Chapter - Statistics and Probability

1. Measures of Discretion: Understanding measures of dispersion is crucial for assessing data variability. In this practice paper, you will work with fundamental measures like mean, median, and mode for both grouped and ungrouped data. 

Mean is calculated as the sum of data points divided by their count. 

Median identifies the middle value in ordered data. Mode reveals the most frequent value, and a dataset can have no mode, one, or more modes.

You will also delve into standard deviation, which quantifies data spread. For ungrouped data, find the differences between data points and the mean, square these, compute the average, and then take the square root. For grouped data, use midpoints and frequencies.

2. Variance and Mean Deviation for both grouped and ungrouped data: In this practice paper, you will explore Variance and Mean Deviation for both grouped and ungrouped data. Variance is a measure of how data points deviate from the mean. For ungrouped data, you find the differences, square them, calculate the average. In grouped data, you'll use group midpoints and frequencies. Mean Deviation, or Average Deviation, quantifies the average difference of data points from the mean. For ungrouped data, you determine the absolute differences and calculate their average. For grouped data, apply the same concept using midpoints and frequencies.

3. Probability of an event: The concept of Probability, which quantifies the likelihood of an event occurring. Probability values range from 0 (impossible) to 1 (certain). For instance, rolling a fair six-sided die yields a $\dfrac{1}{6}$ probability of getting a specific number. The formula for probability, P, is:

$\text{Probability }(P) = \dfrac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$. 

To solidify your grasp of this fundamental concept, you'll engage in various probability problems, exploring the likelihood of different events. 

4. Addition Theorem and the Multiplication Theorem: 

• Addition Theorem of Probability: This theorem helps determine the probability of either of two events occurring. You add the individual probabilities of each event and subtract the probability of both happening simultaneously. For example, it's akin to calculating the chances of drawing either a red or a blue marble from a bag without replacement.

• Multiplication Theorem of Probability: This theorem is employed to find the probability of both of two events happening. You multiply the probabilities of each event. To illustrate, if you aim to calculate the probability of drawing two aces from a deck of cards, you'd multiply the probability of drawing an ace on the first attempt by the probability of drawing an ace on the second try. These theorems are essential for mastering probability concepts in the JEE Main Math exam.

5. Bayes’ Theorem: Bayes' Theorem is a powerful tool for solving probability problems involving conditional probability. It helps you update your beliefs or predictions when new information becomes available.

Simply put, Bayes' Theorem calculates the probability of an event A happening, given that event B has already occurred. It's expressed as:

$P(A|B) = \dfrac{[P(B|A) \times P(A)]}{P(B)}$,

Where,

• P(A|B) is the probability of A given B.

• P(B|A)is the probability of B given A.

• P(A) and P(B) are the probabilities of A and B independently.

6. Probability distribution of a random variate: Think of this distribution as a road map that illustrates how the values of a random variable are distributed. It outlines the probability of each possible outcome. For instance, when rolling a six-sided die, the probability distribution provides the likelihood of obtaining a 1, 2, 3, 4, 5, or 6.

7. Bernoulli trials: Think of Bernoulli trials as a series of independent experiments, each having two possible outcomes known as "success" and "failure." For instance, when flipping a fair coin, landing on heads is considered a "success," while landing on tails is a "failure."

Each trial in Bernoulli trials has the same probability of success, labeled as 'p,' and the same probability of failure, labeled as 'q' (where q = 1 - p). These trials serve as the foundation for more complex probability models and are instrumental in analyzing and predicting the likelihood of achieving a specific number of successes in a sequence of such trials.

8. Binomial distributions: The binomial distribution allows you to determine the probability of achieving a specific number of successes in a fixed number of trials. It is defined by two critical parameters: 'n' (representing the number of trials) and 'p' (indicating the probability of success in a single trial). For example, you can apply the binomial distribution to calculate the likelihood of obtaining precisely 3 heads in 5 coin flips.

Important Formulas from Statistics and Probability

Descriptive Statistics:

1. Mean (Average):

Population Mean ($\mu$) = $\dfrac{\sum{x}}{N}$

Sample Mean ($\bar{x}$) = $\dfrac{\sum{x}}{n}$

2. Median:

For an odd-sized dataset: Median = Middle Value

For an even-sized dataset: Median = $\dfrac{\text{Value at } \dfrac{n}{2} + \text{Value at } \dfrac{n}{2+1}}{2}$

3. Mode:   

The mode is the most frequently occurring value in a dataset.

4. Range:

Range = Maximum Value - Minimum Value

5. Variance:

Population Variance ($\sigma^2$) = $\dfrac{\sum{(x - \mu)^2}}{N}$

Sample Variance ($s^2$) = $\dfrac{\sum{(x - \bar{x})^2}}{n-1}$   

6. Standard Deviation:

Population Standard Deviation ($\sigma$) = $\sqrt{\sigma^2}$

Sample Standard Deviation ($s$) = $\sqrt{s^2}$

Probability:

7. Probability of an Event:

$P(A) = \dfrac{\text{Number of Favorable Outcomes}}{\text{Total Number of Possible Outcomes}}$

8. Complement Rule:

$P(A') = 1 - P(A)$

9. Multiplication Rule (for Independent Events):

$P(A \text{ and } B) = P(A) \cdot P(B)$

10. Addition Rule (for Mutually Exclusive Events):

$P(A \text{ or } B) = P(A) + P(B)$

Conditional Probability:

11. Conditional Probability:

$P(A | B) = \dfrac{P(A \text{ and } B)}{P(B)}$

Bayes' Theorem:

12. Bayes' Theorem:

$P(A | B) = \dfrac{P(B | A) \cdot P(A)}{P(B)}$

Random Variables:

13. Expected Value (Mean) of a Random Variable:

$E(X) = \sum(x \cdot P(X=x))$

14. Variance of a Random Variable:

$\text{Var}(X) = E((X - \mu)^2) = \sum((x - \mu)^2 \cdot P(X=x))$

15. Standard Deviation of a Random Variable:

$\sigma(X) = \sqrt{\text{Var}(X)}$

Probability Distributions:

16. Binomial Probability Distribution:

$P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}$

17. Normal Distribution:

The probability density function of the normal distribution is given by:

$f(x) = \dfrac{1}{\sigma\sqrt{2\pi}} \cdot e^{-\dfrac{(x - \mu)^2}{2\sigma^2}}$

18. Poisson Distribution:

$P(X = k) = \dfrac{e^{-\lambda} \cdot \lambda^k}{k!}$

19. Exponential Distribution:

$f(x) = \lambda \cdot e^{-\lambda x}$

Hypothesis Testing:

20. Z-Score:

$Z = \dfrac{X - \mu}{\dfrac{\sigma}{\sqrt{n}}}$

21. T-Score (used in Student's t-distribution):

$t = \dfrac{\bar{x} - \mu}{\dfrac{s}{\sqrt{n}}}$

22. Chi-Square Test:

$\chi^2 = \sum{\dfrac{(O - E)^2}{E}}$, where $O$ is the observed frequency, and $E$ is the expected frequency.

JEE Main Maths Practice Papers on Statistics and Probability - PDF Download

JEE Main Maths Practice Papers on Statistics and Probability PDF is a resource that provides a variety of questions on the topic, which can help students improve their problem-solving skills and develop a better understanding of the concepts. Here's what you can expect from JEE Main Maths Practice Papers on Statistics and Probability in PDF format:

Types of Questions: JEE Main Maths Practice Papers on Statistics and Probability cover a variety of questions, including multiple-choice questions, numerical-based questions, and assertion-reasoning questions. These questions are designed to test students' understanding of the concepts and principles of Statistics and Probability.

Difficulty Level: JEE Main Maths Practice Papers on Statistics and Probability come with questions of varying difficulty levels. These practice papers have both easy and difficult questions, which can help students prepare for the exam and improve their problem-solving skills.

Detailed Solutions: JEE Main Maths Practice Papers on Statistics and Probability come with detailed solutions and answer keys. These solutions can help students understand the concepts better and identify their mistakes. The answer keys also help students evaluate their performance and identify areas where they need to improve.

Vedantu's Maths Daily Practice Problems for JEE Main - Now with Statistics and Probability!

Vedantu provides the best practice problems for JEE Main Maths. Our carefully selected problems cover all the important concepts, helping you enhance your speed and accuracy. To cater to your specific needs, we offer chapter-wise and topic-wise practice problems, allowing you to focus on the areas where you require the most assistance.

Here are some of the benefits of solving Maths Statistics and Probability  Daily Practice Problems for JEE Main:

Exposure to Exam-style Questions: By solving our Statistics and Probability  practice problems, you gain valuable exposure to the types of questions commonly asked in the JEE Main exam.

Enhanced Conceptual Understanding: Regular practice helps strengthen your understanding of mathematical concepts, enabling you to tackle a wide range of problems confidently.

Improved Speed and Accuracy: Through consistent problem-solving, you develop the necessary skills to solve questions efficiently, improving your speed and accuracy during the exam.

Identification of Weaknesses: By solving a variety of problems, you can identify areas where you need additional practice and focus your efforts accordingly.

If you are determined to achieve a good score on the JEE Main exam, solving Vedantu's Maths Statistics and Probability  Daily Practice Problems is a must. Our practice problems offer the ideal opportunity to acquire the practice necessary for success.

To make the most of your Maths Statistics and Probability  Daily practice problems (DPPs), consider the following tips:

Start with Easy Problems: Begin your practice with easier problems to build confidence and establish a productive rhythm.

Gradually Increase Difficulty: As you gain comfort, gradually challenge yourself with more difficult problems to expand your problem-solving abilities.

Comprehend Concepts: Understand the underlying concepts of the problems you solve. This comprehension will enable you to tackle similar questions correctly on the actual exam.

Time Management: Time yourself while solving problems to improve your speed. This practice will assist you in effectively managing your time during the exam.

Seek Help When Needed: Don't hesitate to seek guidance or clarification when you encounter difficulties. Utilize available resources such as teachers and Vedantu's doubt-solving sessions.

Solving daily practice problems is an integral part of JEE Main Maths Statistics and Probability  preparation. To secure a good score on the exam, it is crucial to ensure you have sufficient practice. Vedantu's practice problems provide the perfect opportunity to acquire the practice you need to succeed.

Start solving Maths Statistics and Probability  Daily Practice Problems today and empower yourself for success in the JEE Main exam!