How to study Probability for Class 12?
To start with, you'll learn the basic definition of Probability and how to apply it in problem solving. You need to keep in mind that probability=(number of favourable events)/total number of events. You'll learn about Conditional Probability, Mutually exclusive and independent events and properties regarding these.
Moving on, you learn about Total Probability and how it leads to Bayes' Theorem. There area a number of solved examples illustrated here for you to practice. This comes to the end of the first part of the course.
Next, you'll learn what are Random variables and how to calculate the mean and variance of discrete and continuous random variables. The course teaches you how to distinguish between a discrete and continuous variable. Moving on, you'll come to Binomial distributions and how to check if a variable is a random variable or follows Binomial distribution.
This is extremely important and the course teaches you how to distinguish between the two. Learn how to calculate the mean and variance of random variables and a Binomial distribution. You're also given all the formulas taught in the course as one module.
Bonus-Learn about the Poisson Distribution in Probability. You'll learn about the mean and variance of the Poisson distribution and its application in problems.
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You may have come across questions in Probability where each question follows a different approach. I am a mathematics teacher and coach, having taught Maths at the high school and college level for three decades and I can empower you with a good knowledge of Probability.
You need to have a basic knowledge of Probability, which you have learnt in Class 11. Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes. You learn the addition theorem of Probability.
Which point to keep in mind while problem solving?
A useful point to keep in mind while solving problems in Probability is to draw Venn diagrams depicting sets. You also need to know DeMorgan's laws. In this context, you will need to learn about complement of a set.
An Important point to note is that probability of any event cannot exceed one and cannot be negative.You would also need to have a knowledge of Permutations and Combinations while problem solving questions in Probability. Next, you will need to learn about Mutually exclusive and exhaustive events. Two events are said to be independent if the occurrence of one event does not affect the other. In this context, you have the Multiplication Theorem on Probability. What is Conditional Probability? You'll learn how to calculate the probability of a given event A given that event B has occurred P(A/B). There are a number of questions which can be asked in this context. You can refer to my links below to learn more.
That takes us to the law of Total Probability which holds for a number of mutually exclusive and exhaustive events and an event A which is associated with the sample space.
How to understand Bayes Theorem?
Bayes Theorem is a beautiful application of this. Problems in Bayes theorem are easy to solve and all my students get it right.
What are Random variables?
Coming to random variables, a random variable is a variable whose values are determined by chance. You'll learn how to calculate the probability distribution of a random variable and how to calculate it's mean and variance. Note that mean is also called Expectation of the variable and variance is the square root of standard deviation. Lastly, you have a Binomial distribution.
How will you distinguish between a random variable and Binomial variable?
. A Binomial experiment is any experiment that can be a sequence of n trials where the trials are finite The result of any trial is independent of the other trials. as, I tell my students, for a Binomial distribution, it is with replacement. Each trial has only 2 possible outcomes, head and tail.
You can contact me for online tutoring if you need extra help. I can help you on a one to one basis or you can join with your fellow students and learn.
What extra resources will you be needing?
You can purchase a question bank on Probability which covers a variety of questions including multiple choice question, Assertion based questions, Case study based questions, conceptual based questions, short answer questions and long answer questions.What's more, I can correct your answers, so you'll know where you stand. You can also purchase formula flashcards which makes learning fun.
How are you benefiting?
You can access the free resources in the form of youtube videos or sign up for a question bank, formulas or online tutoring. You deserve the best.
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