Probability for Beginners : Building a Foundation (Part 2)

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Build up your confidence to state and establish the addition theorems on probability and use them in solving problems.

36 students enrolled

What Will I Learn?

- 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.

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.

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

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

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!*

Who 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.

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Curriculum For This Course

17 Lectures

01:07:21
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Introductory Lecture
1 Lecture
03:58

Overview of what we will cover in the course.

Preview
03:58

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Theorems on basic laws of probability.
2 Lectures
07:06

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.

Preview
03:00

Test your understanding _Lecture 2

3 questions

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.

Theorem 2 on basic laws of probability

04:06

Test your understanding_Lecture 3

3 questions

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Addition theorems on probability
4 Lectures
19:02

In this video the proof of addition theorem for any two events associated with a random experiment having equally likely outcomes will be discussed.

Theorem 3: Addition theorem for two events.

03:29

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

Theorem 4: Addition theorem for mutually exclusive events.

05:12

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.

Theorem 5: Addition theorem for mutually exclusive and exhaustive events

02:50

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

Theorem 6: Addition theorem for three events

07:31

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Theorems on odds of an event and occurrence of a complementary event.
6 Lectures
18:53

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.

Odds of an event

02:31

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.

Preview
02:21

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

Theorem 8: Theorem on odds of an event

03:23

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.

Theorem 9: Results on occurrence of a complementary event.

06:03

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.

Theorem 10: Application of addition theorem for two events .

02:00

In this video we establish the result for the occurrence of probability of exactly one of the two given events.

Theorem 11: Application of theorem 3 and theorem 9.

02:35

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Problem solving section
3 Lectures
17:07

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)

Use of probability in solving coin and die problem

09:30

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.

Preview
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.

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

Problem based on combinations or selections

04:05

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Interactive Quiz section
0 Lectures
00:00

Multiple choice type

17 questions

Multiple choice type

Multiple choice type:

5 questions

True or False

8 questions

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Course wrap-up
1 Lecture
01:15

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

Conclusion

01:15

About the Instructor