Probability for Beginners : Building a Foundation (Part 2)

Build up your confidence to state and establish the addition theorems on probability and use them in solving problems.
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  • Lectures 17
  • Length 1 hour
  • Skill Level All Levels
  • Languages English
  • Includes Lifetime access
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About This Course

Published 3/2015 English

Course Description

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 K-11 and K-12 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!

Good Luck!

What are the requirements?

  • Knowledgeof basic algebra
  • Definition of probability. Understanding of the terms experiment, random experiment, trial, outcomes, favourable outcomes, equally likely outcomes and sample space.
  • Knowledge of the sample spaces for a deck of playing cards, throwing of a coin (or coins) and throwing a die (or dice).
  • Knowledge of the terms event, occurrence of an event, sure event, impossible event, elementary event and compound event.
  • Understanding of the events .... mutually exclusive, mutually exhaustive , mutually exclusive and exhaustive.
  • Basic set theory concepts, able to understand Venn diagrams, understanding of Union and Intersection of sets, difference of sets, complement of a set.
  • Knowledge of combinations or selections.

What am I going to get from this course?

  • You will be confident to state and establish the addition theorems on probability.
  • You will be able to prove 5 basic laws of probability .
  • State and prove the addition theorem on probability for two and three events..
  • Generalize the addition theorem of probability for mutually exclusive events.
  • Extend the addition theorem of probability for mutually exclusive and exhaustive events.
  • You will gain knowledge about some results on probability of occurrence of a complementary event.
  • Will be able to define odds in favor and odds against an event and hence derive a formula for the same.
  • Will be able to encounter problems based on addition theorems.

What is the target audience?

  • These lectures will be helpful to K-11 and K-12 grade students who want a better understanding of the topic "Addition theorems on probability ".
  • This course is a bonus for people who have keen interest in the subject of Mathematics and also for the people who have great passion for the subject!
  • Anybody who wants to brush up the topic "Addition theorems on probability ", for any competitive exam within a short span of time, this course is strongly recommended.
  • You can as well use quiz at the end of the course to test your skills in the topic "Addition theorems on probability ", before any exam.

What you get with this course?

Not for you? No problem.
30 day money back guarantee.

Forever yours.
Lifetime access.

Learn on the go.
Desktop, iOS and Android.

Get rewarded.
Certificate of completion.

Curriculum

03:58

Overview of what we will cover in the course.

Section 1: Theorems on basic laws of probability.
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.

Test your understanding _Lecture 2
3 questions
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.

Test your understanding_Lecture 3
3 questions
Section 2: Addition theorems on probability
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.

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.

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.

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.
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.

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.

03:23

In this theorem the formulae to find odds in favor and odds against an event is established.

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.

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.

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
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(Ac ), P(Bc ),P(AUB), etc.

(2)Verify that P(A) + P(Ac ) = 1 and P(B) + P(Bc ) = 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)

03:32

In this video the following problem is solved:

A card is drawn at random from a well-shuffled deck of fifty two cards.

Find the probability of its being a heart or a queen.

04:05

In this video the following problem is solved:

A card is drawn at random from a well-shuffled deck of fifty two cards.

What is the probability that either both are black or both are kings.

Section 5: Interactive Quiz section
Multiple choice type
17 questions
5 questions

Multiple choice type

True or False
8 questions
Section 6: Course wrap-up
01:15

This video concludes with what we have done in this course.

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Instructor Biography

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, 2-year IB Diploma (International Baccalaureate) covering AL,SL and HL courses. I have so far made 200+ videos in various Math topics.

Worked for:

FIITJEE EDU SOFT Ltd. as

CHIEF CONTENT MODERATOR under the department of

SYSTEM DEVELOPMENT associated with the project

EDFORA (Education for All) in Gurgaon.

Key Responsibilities held: 1. Overall content direction ( in making educational videos).

2. Managing quality of content created by content contributors.

3. Refining checklist and checklist of content.

4. Leading the team of HODs and Domain Auditors.

5. Creating training collateral for content creators.

6. Establish QA/QC Benchmarks for Videos

7. Work closely with HODs to achieve domain wise targets and drive the process from Review to Publish

8 .Providing overall guidance/ direction to the content team for preparing content for different state boards.[ CBSE, ICSE, ISC, Andhra Pradesh Board, Madhya Pradesh Board, Maharashtra Board, Rajasthan Board, Uttar Pradesh Board]

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