Probability is a very important chapter in JEE syllabus of Mathematics. It is one of those topics which are considered to be relatively tricky than the other topics. But in order to master probability, aspirants need to be confident about this topic.
Most students find this topic to be difficult because their basics are not clear. Here we will learn about the methodologies of computing the probability of an event. But first, we should be familiar with the meaning of probability and then proceed with the tricks related to it.
Examples of Probability:
- Probably it will snow tomorrow
- Brazil is likely to win the football world cup
- It is possible that there will be flood in this area due to heavy rainfall
In each of these following sentences, we can see different degrees of certainty of results which can be calculated with the help of probability.
IIT aspirants preparing for JEE Mains and JEE Advanced should be very thorough with this chapter. It is a very important topic that also sets the stage for jobs in the field of data science, data analysis, and consultancies. Here, we will learn about some tips and tricks on Probability that can help aspirants to prepare for their JEE.
Visualize the problem
Aspirants should try to apply logic in the problem visually by extending it to Sets and Venn Diagrams. If the problem becomes more difficult to understand and has more than 2 to 4 events in it, aspirants can visualize the problem using a Venn Diagram.
Difference between AND / OR
Aspirants should read the question thoroughly and follow each step described in the question. It is essential to understand what the problem is trying to tell. “AND” connecting events in a question indicates multiplication and “OR” indicates addition when students will work out the problem mathematically.
Difference between Mutually exclusive and Independent events
When we say that 2 events are mutually exclusive, it does not mean that the 2 events are independent. Independent events are those which do not depend on each other and mutually exclusive events are the ones that cannot happen at the same time.
Mutually exclusive events X and Y indicates P(X and Y) which occur with zero probability whereas Independent Event X and Y, P(X and Y) occurs with P(X) * P(Y).
Independent Random Variables
If two events or variables are said to be independent they have 0 correlations between them.
For example, if 2 events X and Y are independent, then
P(X|Y) = P(X) that is, the probability of X occurring when the probability of Y is excluded. Therefore P(X∩Y) = P(A) * P(Y).
Application of Bayes Theorem
When the sample space will consist of n mutually exclusive events X1, X2, X3, . . . , Xn and within the sample space, an event A will exist for which P(A)<0; only then aspirants are suggested to use Bayes Theorem.
Write all possible cases
Sometimes formulae, do not always give us results in this chapter. Therefore for problems like Coins, Dices, and Cards, it is better that students write all the possible cases and determine the individual probabilities of each case and then use AND /OR according to the problem.
These kinds of problems are special because it restricts the playing field for students by mentioning that some part of the problem had already occurred. The general equation is:
P(X|Y) = P(X∩Y) /P(Y). This is the probability of X occurring when Y has already occurred.
Probability is not a difficult chapter to master but it is not so easy as well. JEE aspirants should solve more problems on probability to get familiar with all the types of questions. Subscribe to our YouTube Channel to watch interactive videos on important JEE topics.