Probability

This post shall deal with Probability as a topic for preparation of JEE Advanced and JEE Mains. The important topics and nature of questions shall also be discussed.

Importance

Yearly Trend

Probability in itself is one of the most important topics when it comes to preparation of JEE Advanced and JEE Mains, because of the number of questions that appear in the question papers and the number of marks that it carries.

Probability is one of those topics which can fetch you good marks once proper efforts are put into it. The basics need to be very strong and after enough practice, the student should be able to have an idea of approaching the solution on reading the question.
The trends from the previous years’ question papers highlight the importance of this topic. At least 2 questions from Probability have been asked in the last 5 years in JEE Advanced, which sometimes included comprehension type questions, clearly underlining the number of marks that can be scored from this topic. From the JEE Mains perspective, 1-2 questions can be expected, the maximum being 3 questions being asked in 2010.

The important topics and the nature of questions shall be discussed next.

Topics

It can be understood from the weightage of marks, that a wide variety of questions on different topics can be asked from this chapter. So a lot of concepts and approaches need to be studied in the preparation.

The basics of Probability are derived from Permutations and Combinations, so one needs to have a good grip on that chapter. A very common type of question asked is the one related to Sum of all probabilities, in which certain equations are to be solved.
Some of the other important problems are the ones related to arrangement in lines, circular probability (arrangement around a table etc), nature of events (independent or mutually exclusive), union and intersection of events, and multiple probabilities in a single problem.

The single-most important topic to understand is Conditional Probability, where the probability of an event is to be calculated under a set of certain conditions. The formula for conditional probability is given by
!!P(A|B)=(P(AnnnB))/(P(B))!!

Most number of questions will make use of this formula here and there, and hence is important to be well versed with. More the number of questions you solve in the preparation, the easier it will get to solve them in the exam, taking minimum time.