Probability JEE Main Questions: If you want to take admission into top IITs then maths is one such subject which you simply cannot ignore. In JEE Mains Mathematics, probability is one of the most important topics that tests the understanding of students in logic, principles and analytical thinking. Every year, there is a good amount of weightage from this chapter. Questions are mostly moderate level in difficulty and are application based. These questions are designed to assess how well students can apply probability concepts in real life and maths situations. It is considered one of the high scoring topics in the JEE Mains exam so you must be strong in formula and concepts. JEE Main 2026 registration has already started and students can register from 31 October 2025 to 27 November 2025, session 1 is scheduled from 21 to 30 January 2026.
Main Topics of Probability for JEE Mains Questions 2026
Previous Year Questions JEE Mains: Probability
Why Probability is Important in JEE Mains
JEE Main Previous Year Maths Questions With Solutions
Probability JEE Main Questions: PYQs, Weightage, Formulas & Practice
In this article, important questions from Probability are provided that will help you understand the types of questions asked in the JEE Main exam. Questions from concepts like Discrete Random Variable and Variance, Mean deviation about Mean, Standard deviation and Variance are covered. They help to improve conceptual clarity and speed during the exam. Go through the questions carefully, revise the formulas related to these questions, and analyse the logic behind every solution to ensure solid preparation for JEE Mains Mathematics.
Main Topics of Probability for JEE Mains Questions 2026
Probability in JEE Mains covers a variety of concepts that test your reasoning and mathematical understanding. These questions are designed to check how to apply formulas and solve questions. The following are some main topics of Probability JEE Mains questions with solutions asked in previous years:
Amrita University B.Tech 2026
Recognized as Institute of Eminence by Govt. of India | NAAC ‘A++’ Grade | Upto 75% Scholarships
Solving previous year questions from probability is one of the best ways to prepare for the JEE Main exam. These questions help you to understand the exam pattern and the types of questions asked. Given below some previous year questions of JEE Mains from Probability:
Question: A box contains 10 pens, of which 3 are defective. A sample of 2 pens is drawn at random, and let X denote the number of defective pens. Then the variance of X is
(1) $\frac{11}{15}$
(2) $\frac{28}{75}$
(3) $\frac{2}{15}$
(4) $\frac{3}{5}$
Solution: Discrete Random Variable and Variance Calculation
The concept involves using a discrete random variable $X$ with a given probability distribution $P(X = x_i)$. The mean (expected value) is calculated using:
Download the JEE Main 2026 Preparation Tips PDF to boost your exam strategy. Get expert insights on managing study material, focusing on key topics and high-weightage chapters.
Question: Let the mean and the standard deviation of the observation $2,3,3,4,5,7, \mathrm{a}, \mathrm{b}$ be 4 and $\sqrt{2}$ respectively. Then the mean deviation about the mode of these observations is :
$N$ is the sum of all frequencies
Then, find the deviations of observations $x_i$ from the mean $\bar{x}$ and take their absolute values, i.e., $\left|x_i-\bar{x}\right|$ for all $i=1,2, \ldots, n$
After this, find the mean of the absolute values of the deviations
$\operatorname{M.D.}(\bar{x})=\frac{\sum_{i=1}^n f_i\left|x_i-\bar{x}\right|}{\sum_{i=1}^n f_i}=\frac{1}{N} \sum_{i=1}^n f_i\left|x_i-\bar{x}\right|$
Mean Deviation About any value 'a'
$
\text { M.D.(a) }=\frac{1}{\mathrm{~N}} \sum_{i=1}^n f_i\left|x_i-\mathrm{a}\right|
$
Mean deviation for a grouped frequency distribution
The formula for mean deviation is the same as in the case of an ungrouped frequency distribution. Here, $x_i$ is the midpoint of each class.
Standard deviation
The standard deviation is a measure of the amount of variation or dispersion in a set of values. It quantifies how much the values in a data set deviate from the mean (average) value. A low standard deviation indicates that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range.
For a data set with values $x_1, x_2, \ldots, x_n$ and mean $\bar{x}$, the {population standard deviation is defined as
$\begin{aligned} &2=\frac{4+1+1+0+1+9+(a-4)^2+(b-4)^2}{8} \\ & 16=48+a^2+b^2-8 a-8 b \\ & a^2+b^2=32 \\ & 32=2 a b \\ & a b=16 \\ & a=4, b=4 \\ & \text { mode }=4 \\ & \text { mean deviation }=\frac{2+1+1+0+1+3+0+0}{8}=1\end{aligned}$
Hence, the answer is option (1).
Question: Let the Mean and Variance of five observations $x_1=1, x_2=3, x_3=a, x_4=7$ and $x_5=b, a>b$, be 5 and 10 respectively. Then the Variance of the observations $n+x_n, n=1,2, \ldots \ldots \ldots 5$ is
(1) 17
(2) 16.4
(3) 17.4
(4) 16
Solution: Variance
The mean of the squares of the deviations from the mean is called the variance and is denoted by $\sigma^2$ (read as sigma square).
Variance is a quantity which leads to a proper measure of dispersion.
The variance of $n$ observations $x_1, x_2, \ldots, x_n$ is given by
Question: The variance of the numbers $8,21,34,47, \ldots, 320$, is____________.
Solution: The mean of the squares of the deviations from the mean is called the variance and is denoted by $\sigma^2$ (read as sigma square).
Variance is a quantity that leads to a proper measure of dispersion.
The variance of $n$ observations $x_1, x_2, \ldots, x_n$ is given by
Question: For a statistical data $x_1, x_2, \ldots, x_{10}$ of 10 values, a student obtained the mean as 5.5 and $\sum_{i=1}^{10} \mathrm{x}_{\mathrm{i}}^2=371$. He later found that he had noted two values in the data incorrectly as 4 and 5 , instead of the correct values 6 and 8 , respectively. The variance of the corrected data is
(1) 7
(2) 4
(3) 9
(4) 5
Solution: Variance
The mean of the squares of the deviations from the mean is called the variance and is denoted by $\sigma^2$ (read as sigma square).
Variance is a quantity which leads to a proper measure of dispersion.
The variance of $n$ observations $x_1, x_2, \ldots, x_n$ is given by
Number of data points: $n=10$
Incorrect mean: $\bar{x}_{\text {wrong }}=5.5$
$\sum_{i=1}^{10} x_i^2=371$ (sum of squares of the incorrect data)
Two values were recorded incorrectly as 4 and 5, but the correct values are 6 and 8
The incorrect sum of values using the mean:
$
\sum x_i=10 \times 5.5=55
$
Corrected sum $=55-(4+5)+(6+8)=55-9+14=60$
Corrected mean:
$
\bar{x}_{\text {correct }}=\frac{60}{10}=6
$
Original incorrect squared sum:
$
\sum x_i^2=371
$
Remove the incorrect squares, add the correct ones:
Probability is an important part of JEE Main Maths because questions from this chapter come every year in the exam. If the basics from this chapter are well prepared then it is an easy and scoring chapter that will help you improve your overall marks. Given below some point on why this chapter is important for JEE Mains:
1.This chapter is less time consuming and can be covered with proper efficiency and attention.
2. Every year this chapter has a significant amount of weightage associated with it. Probability JEE Mains questions with solutions can increase your rank too if studied properly.
3. It is linked with chapters like Permutation and combination, Sets, Relations. This can help you keep the flow and understand concepts better.
4. In JEE Advanced, it has core importance as this forms the base of mathematical reasoning.
5. Probability JEE Mains weightage is approximately 6.32% which cannot be ignored.
JEE Main Previous Year Maths Questions With Solutions
Solving previous year questions is one of the best ways to prepare for the JEE Main exam. These questions help you to understand the exam pattern and the types of questions asked. Solving these questions improves your problem solving speed and accuracy. To find the probability PYQs you can download the ebooks given below for practice anytime.
Q: Is Probability an important topic for JEE Main?
A:
Yes, Probability is an important topic in JEE Main Mathematics. It carries a good weightage every year and is considered a high-scoring chapter if the concepts and formulas are well understood. It also links with other chapters like Permutations & Combinations and Sets.
Q: Is Probability difficult for JEE Main?
A:
Not really. It is considered moderate in difficulty and requires strong basics in formulas and logic.
Q: How many questions are asked from Probability in JEE Main?
A:
1-2 questions are asked constituting 4-8 marks.
Q: What are the main topics of Probability in JEE Main?
A:
The core concepts of probability are Bayes theorem, random variables, binomial distribution and basic terms/events.
You want to prepare for JEE Mains in 2 months. Don't worry you still make the most of your preparation with a smart strategy. You can check out these detailed tips and tricks from Careers360 including important topics, revision strategies, and ways to improve your speed and accuracy.
Currently, there is no official release of JEE Mains 2026 registration begin. But on an average, every year there will be
11 Lakh to 12.5 Lakh
students
register
If you belong to the BC (Backward Class) category, you can choose OBC-NCL in JEE Mains only if your caste is included in the Central OBC list released by the Government of India.
Here’s how it works:
Central OBC list: Used for national-level exams like JEE, NEET, UPSC, etc.
State BC list: Used only for state-level admissions or jobs.
So, if your BC caste name is in the Central list, select OBC–NCL while filling the JEE form.
If your caste is not in the Central list, choose General category, because the state BC certificate won’t be valid for JEE.
Example:
If you’re BC in Tamil Nadu but your caste isn’t in India’s Central list, you’ll be counted as General for JEE.
No, it’s not compulsory to fill the APAAR ID in the JEE Main application form right now.
If your APAAR ID shows a “credential mismatch” error even after entering the correct number, don’t worry, you can simply leave it blank and continue filling the form.
The APAAR ID field is optional for most students.
It’s mainly for linking your academic records under the Academic Bank of Credits (ABC) system.
The mismatch often happens if your Aadhaar details or school record name format differ.
So, you can submit your JEE form without the APAAR ID, and it won’t affect your application.
A flight attendant ensures passenger safety and comfort during flights. Key duties include conducting safety checks, assisting passengers, serving food and drinks, and managing emergencies. They must be well-trained in safety procedures and customer service. A high school diploma is typically required, followed by rigorous training to qualify for the role.
A Flight Engineer monitors and operates an aircraft’s complex systems like engines, fuel, and hydraulics during flight, ensuring optimal performance and safety. They assist pilots with technical issues, conduct inspections, and maintain records. This role requires strong technical knowledge, problem-solving, and communication skills. Training usually involves a degree in aviation or aerospace engineering and specialised certification.
An Aircrew Officer operates and navigates aircraft, ensuring safe flights and compliance with aviation regulations. Key duties include managing flight systems, conducting pre- and post-flight checks, and adhering to safety standards. The role typically requires working five days a week, with around 120 flight hours monthly. Employment may be contractual or permanent, depending on the airline.
An aerospace engineer designs, develops, tests, and maintains aircraft, spacecraft, and related systems. They apply physics and engineering principles to improve aerospace technologies, often working in aviation, defence, or space sectors. Key tasks include designing components, conducting tests, and performing research. A bachelor’s degree is essential, with higher roles requiring advanced study. The role demands analytical skills, technical knowledge, precision, and effective communication.
An air hostess, or flight attendant, ensures passenger safety and comfort during flights. Responsibilities include safety demonstrations, serving meals, managing the cabin, handling emergencies, and post-flight reporting. The role demands strong communication skills, a calm demeanour, and a service-oriented attitude. It offers opportunities to travel and work in the dynamic aviation and hospitality industry.
An aeronautical engineer designs, develops, tests, and maintains aircraft and related systems. They work on components like engines and wings, ensuring performance, safety, and efficiency. The role involves simulations, flight testing, research, and technological innovation to improve fuel efficiency and reduce noise. Aeronautical engineers collaborate with teams in aerospace companies, government agencies, or research institutions, requiring strong skills in physics, mathematics, and engineering principles.
A Safety Manager ensures workplace safety by developing policies, conducting training, assessing risks, and ensuring regulatory compliance. They investigate incidents, manage workers’ compensation, and handle emergency responses. Working across industries like construction and healthcare, they combine leadership, communication, and problem-solving skills to protect employees and maintain safe environments.
An airline pilot operates aircraft to transport passengers and cargo safely. Responsibilities include pre-flight planning, in-flight operations, team collaboration, and post-flight duties. Pilots work in varying schedules and environments, often with overnight layovers. The demand for airline pilots is expected to grow, driven by retirements and industry expansion. The role requires specialized training and adaptability.
1 Jobs Available
Never miss an JEE Main update
Get timely JEE Main updates directly to your inbox. Stay informed!
