Probability for Beginners : Building a Foundation (Part 2)
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This course is for beginners who want to learn the fundamentals of probability.
The course begins with some basic laws of probability, and moves on to introduce the addition laws or theorems on probability.
These videos are designed to give a clear understanding of the proofs for addition laws or theorems on probability. Building on probability concepts that begin in the middle grades, students of K11 and K12 grades use the language of set theory to expand their ability to extend the concept of addition theorems to problem solving.
The lectures also cover some results on probability of occurrence of a complementary event.
Also a brief discussion on odds of an event followed by a theorem on the same is covered in two of the videos. Appropriate examples are also discussed.
These videos will remove the doubts and clear the confusion between the terms "probability" of an event happening and "the odds" of an event.
The videos can be completed in an hour.
Five interactive quizzes are added to the course. The quizzes are of two types.
Type one is multiple choice quiz where only one of the answers provided is correct. and
Type two is true or false quiz. The problems in these quizzes should give you an idea about the type of problems that you can encounter in your exams.
All questions are not direct. The solutions to some of them can be obtained by using more than one law or theorem.
There is no time limit for the quiz. You can take the quiz at your own pace. However, it is advisable that a time limit be set in order to judge your speed of completing the quiz. This will help you in the preparation for actual examination. There is a score keeper for the quiz to track your progress
Get started and gain confidence to state and establish the addition theorems on probability and use them in solving problems by enrolling into this course!
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Lecture 1  03:58  
Overview of what we will cover in the course. 

Section 1: Theorems on basic laws of probability.  

Lecture 2  03:00  
In this video the proof for the following three laws of probability will be discussed: 1. Probability of any event is greater than or equal to zero. 2. Probability of an impossible event is equal to zero. 3. Probability of a sample space is equal to one. 

Quiz 1 
Test your understanding _Lecture 2

3 questions  
Lecture 3  04:06  
In this video the proof for the following two laws of probability will be discussed: If event1 is a subset of event 2 then 1.Probability of event1 is less than or equal to the probability of event 2. 2.The probability of difference of these two events is equal to the difference of their probabilities. 

Quiz 2 
Test your understanding_Lecture 3

3 questions  
Section 2: Addition theorems on probability  
Lecture 4  03:29  
In this video the proof of addition theorem for any two events associated with a random experiment having equally likely outcomes will be discussed. 

Lecture 5  05:12  
In this video the proof of addition theorem for mutually exclusive events associated with a random experiment having equally likely outcomes will be discussed. 

Lecture 6  02:50  
In this video the proof of addition theorem for mutually exclusive and exhaustive events associated with a random experiment having equally likely outcomes will be discussed. 

Lecture 7  07:31  
In this video the proof of addition theorem for three events associated with a random experiment having equally likely outcomes will be discussed. 

Section 3: Theorems on odds of an event and occurrence of a complementary event.  
Lecture 8  02:31  
Under the heading “Odds of an event”, the terms odds in favor and odds against an event are defined. An example is discussed to find the probability of occurrence of an event when odds of the event is known. 

Lecture 9  02:21  
In this video proof of a theorem on probability of occurrence of a complementary event is discussed. An example to illustrate the same is taken up.


Lecture 10  03:23  
In this theorem the formulae to find odds in favor and odds against an event is established. 

Lecture 11  06:03  
In this video the following results for any two events A and B associated with a random experiment having equally likely outcomes are discussed: 1.Probability of occurrence of B only. 2.Probability of occurrence of A only. 3.Probability of occurrence of exactly one of two events A and B. 

Lecture 12  02:00  
In this video we prove a theorem involving the relation between the probabilities of intersection and union, and sum of the probabilities of two events, with the help of addition theorem for two events. 

Lecture 13  02:35  
In this video we establish the result for the occurrence of probability of exactly one of the two given events. 

Section 4: Problem solving section  
Lecture 14  09:30  
In this video the following problem is solved: A coin and a die are thrown. Event A is "getting a tail". Event B is "getting a head and an even number". Event C is "getting an even number". (1)Find P(A), P(B), P(C), P(A^{c} ), P(B^{c} ),P(AUB), etc. (2)Verify that P(A) + P(A^{c} ) = 1 and P(B) + P(B^{c} ) = 1 (3) Are A and B mutually exclusive ? Verify that P(AUB) = P(A)+ P(B) (4) Are A and C mutually exclusive ? Verify that P(AUC) = P(A)+ P(C)  P(A intersection B) 

Lecture 15  03:32  
In this video the following problem is solved: A card is drawn at random from a wellshuffled deck of fifty two cards. Find the probability of its being a heart or a queen. 

Lecture 16  04:05  
In this video the following problem is solved: A card is drawn at random from a wellshuffled deck of fifty two cards. What is the probability that either both are black or both are kings. 

Section 5: Interactive Quiz section  
Quiz 3 
Multiple choice type

17 questions  
Quiz 4  5 questions  
Multiple choice type 

Quiz 5 
True or False

8 questions  
Section 6: Course wrapup  
Lecture 17  01:15  
This video concludes with what we have done in this course. 
I am Mathematics Subject Matter Expert.
I am a certified (post graduate trained) mathematics instructor (private tutor) with over 24 years of teaching experience to middle school, high school, senior secondary level and intermediate level covering various school boards including CBSE, ICSE, ISC, IGCSE, 2year IB Diploma (International Baccalaureate) covering AL,SL and HL courses. I have so far made 200+ videos in various Math topics.
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