Probability – 11 Problem types that can come in IIT JEE - JEE Main 2025

PRACBEE REVISION PROGRAM

Probability is a very important but confusing topic in Mathematics. A lot of students struggle with the nuances and smaller details of this chapter. Making this video of Probability took tremendous amount of effort to build up as well. In order to make this chapter super simple, we have started this video with weightage of Probability in JEE and then we systematically go into the syllabus comparison between JEE Main 2024 and JEE Main 2025. This will ensure you have an exact idea of the differences.

Then we will jump into the Mind map of the chapter, so you know which topics and subtopics are covered in Probability chapter for IIT JEE - JEE Main and JEE Advanced, and how these are interlinked with each other. That helps you cover the entire Probability chapter comprehensively and ensure you do not miss any single subtopic or concept from it.

then we'll go into 11 problem type categories in which I have classified all the last 5 to 10 years of questions that came in JEE Main. Since the video has 5-6 questions from each of the 13 types of problems in Probability, mostly from Past Year Questions of JEE Main, we are keeping 2 questions per type in the blog. We will add the list of the 11 problem types followed by 2 questions from each type.

For every topic we will go into the subtopics that need to be covered then go into more deeper points of what exactly there is in the syllabus using Mind maps and ultimately come on to the 11 problem types that can be asked in Probability chapter.

Before we start this video there is a “do” and there is a “don't”. The “do” is do not watch this video like you are watching a movie but keep making notes, keep solving questions, pause the video and see how you can arrive on an answer and develop your approach while solving. The “don't” is that this video is not meant for a fresher student who has not just done Probability. We will not go into very Basics but yes, I will tell you the concept wherever and whenever it is required.

Probability is one such topic in JEE mathematics where most of the students when they attempt three questions, they will only get one question right. Now this problem we encounter because of a very fundamental flaw in their conceptual thinking process. We think that probability is primarily based on PNC. However, this generates a problem that every question that they're doing in probability they're applying the same techniques

that they learnt in P&C chapter, and that is the reason they will only be able to get 1/3rd of the question right because only 1/3rd of the chapter is based on P&C.

So, if you look into Probability, there are three very important parts of the chapter. The first is Classical probability. The problems which are based on classical probability will largely be solved using techniques of P&C only. But if you move towards the second part, that is Axiomatic Probability. There you need to apply axioms in order to solve problems. So, your thinking process should be out of the five axioms that are present with me and one basic premise of classical, which one of these to apply to get to an answer.

Right now, if you think in this manner in this Axiomatic problem, then your chances of getting question correct will be more. If you move towards the next part then there is Statistical Probability. Here again your mindset should be you should understand what is the concept of a Random variable, how to make a Probability distribution table, how to find mean and variance and then solve questions using only these constructs of Statistics.

So, if you get these three parts right, first based on P&C, second based on axioms and the third based on statistics then 100% of questions in this chapter can be solved correctly.

In order to make your life extremely simple for his chapter in JEE, we have divided these three areas into 11 problem types. I will give you the systematic theoretical basis thinking process in each of these 11 problem types, giving you tangible techniques to handle such problems. If you watch this video till the end, I can ensure you that you will get your 100% problems based on Probability right.

So, without any further delay let us start with the weightage of Probability. It is 1 question in every JEE Main paper. It may differ from attempt to attempt.

If you see the syllabus of 2023 and 2024, you can see there is a major change in the syllabus. Bayes’ theorem is no more there in the syllabus. Bernoulli’s theorem and BT distribution is also not there in the syllabus. These earlier used to be a very important part.  Apart from that probability of an event addition and multiplication theorems, Baye’s theorem probability distribution, mean and variance etc are missing.

Mindmap of the chapter – Probability

Now if I start with the Mindmap and go into the actual syllabus of JEE, the actual syllabus of JEE revolves around three very important ideas. The first is Classical probability, the second is Axiomatic probability and the third is Empirical or statistical probability.

These are three major heads in this chapter. If you look into the first head, it generally consists of three very important types of problems - there are problems which are based on P&C. These are the P&C problems only and you can check our P&C video for all such problem types in detail. These are asked in the garb of Probability, so these are the same questions but asked in slightly different manner. So, the method of solving all these questions remains exactly the same. The second important type of question is questions based on odds in favour and against. This is a term that you need to understand what does it mean and then there are questions based on set theory or Venn diagrams. Then if you look into the second part of this chapter that is Axiomatic probability, that is the concept of Kolmogorov’s basic Axioms. So, there are three or four basic axioms of Kolmogorov and the way we do probability. So, these are very important and then there are areas like Conditional probability, multiplication theorem independent events.

And then we move towards the idea of Total probability and Baye’s theorem. These five ideas that we have done here and plus this one idea of Kolmogorov sums up the idea of Axiomatic Probability.

Then comes a very important part of this chapter that is Statistical Probability. It consists of two major parts - the first is the concept of probability distribution and random variable. So we understand what is a random variable, we move towards measuring its probability distribution and there in we come up with the concept of expectancy or mean and variance. On these two ideas JEE has asked a lot of questions and then there is this last idea that is out of the syllabus that is of Bernoulli’s theorem and binomial probability distribution.

Now if we look into the weightage of these chapters in these three areas, you can see lots of questions are usually asked in classical probability because those are questions of P&C only.  Second traditionally Axiomatic probability has been a very important area but in recent years Statistical Probability has become more important.

Problem Types discussion

If you like this video, you may also like Pracbee’s unique 1:1 Last Mile Journey program. In this program we sit with the student to understand their preparation till this point of time. Then we understand how your JEE Main attempt 1 of 2025 has gone. Based on this information, in step two we create a customized planner just for you to help you optimize your marks in JEE Mains attempt two based on whatever preparation you have done and how your first attempt has gone. In step three we schedule session with you 1:1 by a set of faculties aligned by Pracbee and help you implement the customized plan that we wrote for you.

Students have come to us with limited or decent preparation and all have been able to score their marks to a large extent. In 2024, Asesh using this program was able to improve his fortunes by a lot starting from 95% in JEE Mains attempt 1 to getting selected for Mechanical Engineering in IIT Madras finally. Ditya over a period of time was able to crack JEE Advance using this program. If you think that this seems interesting to you, click on the link below in the description, fill the required details and somebody from my team will get in touch with you.

Also, you can drop a comment on the video or write a review of this article. You can also let us know what more we can do for you to make your final 2 months preparations very smooth and effective

All the best for your JEE Main 2025.