Axiomatic Probability - Mathematics

Name: Axiomatic Probability - Mathematics
Rating: 4.3 (54 reviews)

Understanding Axiomatic Approach to Probability in Mathematics

Created byGreat IT Courses

Last updated 11/2019

English

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What you'll learn

Axiomatic Approach to Probability
Definition of Random Experiments, Outcomes, Sample Space, Events,
Algebra of Events
Calculating the Probability of an Event Using the Axiomatic Approach to Probability
Solving Problems Related to Axiomatic Approach to Probability
Learning How to Use Concepts and Reasoning to Reason You Way Through Problems Logically Rather than Memorization

Course content

5 sections • 49 lectures • 24h 51m total length

Instructor Introduction3:21
Meet the instructor, John Rushin Yan, sharing a decade of mathematics experience and a passion for logic, and inviting your feedback to enhance this axiomatic probability course.
Course and Road Map Info1:27

Course Overview and Review37:09
In this video, we will talk about the properties of empirical probability and theoretical probability and why it's necessary to learn the axiomatic approach to probability.
Random Experiment, Sample Space, Sample Point37:18
In this video, we will define the terms mentioned in the video title and also discuss a couple of examples related to them.
Random Experiment, Sample Space, Sample Point Examples14:23
Events29:12
In this video, we will define events based on a typical experiment.
Occurrence and Types of Events37:24
In this video, we will talk about the occurrence of an event. We'll also talk about Impossible events, Sure events, Simple events and compound events that are different types of events.

Complementary Events30:31
In this video, we will talk about complementary events. We'll also talk about some common concepts related to sets such as intersection, union, etc. that will be used in the next videos.
Events A or B, A and B, A but not B33:59
Explain A union B, A intersection B, and A minus B with Venn diagrams and a dice example; show how A or B and A but not B define events.
Mutually Exclusive and Exhaustive Events37:48
Mutually Exclusive Events - Example 727:14
Explore identifying mutually exclusive events in a two-dice experiment by forming sets for even sums, multiples, and comparisons, and determine which pairs have empty intersections (C and D).
Mutually Exclusive and Exhaustive Events - Example 822:34
Three coin tosses yield A: no heads, B: exactly one head, and C: at least two heads; they are mutually exclusive and exhaustive, partitioning the sample space.

Functions and Relations Review33:53
In this video, we'll do a quick review of the concept of functions and relations since it's going to be used in one the upcoming definitions.
Axiomatic Approach to Probability #130:20
Axiomatic Approach to Probability #234:12
Explore the axiomatic approach to probability, defining a real-valued p on the sample space with range 0–1 and total 1, and summing outcomes for events.
Axiomatic Approach to Probability #319:06
Explore the axiomatic approach to probability by assigning nonnegative probabilities to outcomes that sum to one. See how heads and tails and biased distributions fit the framework.
Probability of an Event #121:14
In this video, we will use an example to show how to calculate the probability of an event using the axiomatic approach to probability.
Probability of an Event #28:17
In this video, we will use an example to show how to calculate the probability of an event using the axiomatic approach to probability.
Probability of Equally Likely Outcomes40:13
Explain the probability of equally likely outcomes using the ratio of favorable to total outcomes, applying axiomatic definitions with sample space and events, via a coin toss.
Probability of Event "A or B" #135:25
Apply the inclusion–exclusion principle to compute P(A ∪ B) for two coin‑toss events, using P(A ∪ B)=P(A)+P(B)−P(A∩B) with eight equally likely outcomes, yielding P(A)=P(B)=3/8 and P(A∪B)=1/2.
Probability of Event "A or B" #232:12
Learn to prove P(A ∪ B) by splitting into A minus B, A ∩ B, and B minus A, and derive P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
Probability of Event "not A"35:08
Calculating Probability of Events - Examples #126:11
Compute the probability of drawing a diamond from a well-shuffled 52-card deck using equally likely outcomes, and extend the method to not an ace and not a black card.
Calculating Probability of Events – Examples #236:54
Explore calculating probabilities using card examples, including black cards, non-diamonds, complementary events, union and intersection rules, and simple disjoint events applications.
Calculating Probability of Events – Examples #329:14
Example 12 #1
Calculating Probability of Events – Examples #429:57
Example 12 #2
Calculating Probability of Events – Examples #531:27
Example 12 #3
Calculating Probability of Events – Examples #631:25
Example 13
Calculating Probability of Events – Examples #734:05
Example 13 #2
Exercise 16.3 #129:19
Exercise 1 and 2
Exercise 16.3 #231:11
Exercise 3 #1
Exercise 16.3 #328:18
Exercise 3 #2, Exercise 4
Exercise 16.3 #435:33
Exercises 5, 6, 7
Exercise 16.3 #529:32
Exercises 7, 8, 9, 10, 11, 12
Exercise 16.3 #635:12
Exercises 13, 14, 15, 16, 17, 18
Exercise 16.3 #729:52
Exercises 19 and 20
Exercise 16.3 #831:47
Exercise 21

Miscellaneous Examples #140:47
Example 14 #1
Miscellaneous Examples #236:05
Example 14 #2
Miscellaneous Examples #330:36
Example 15 #1
Miscellaneous Examples #437:24
Example 15 #2
Miscellaneous Examples #524:37
Example 16
Miscellaneous Examples #626:30
Example 17
Miscellaneous Exercises #141:37
Exercise 1
Miscellaneous Exercises #237:49
Exercise 2
Miscellaneous Exercises #338:46
Exercise 3 and 5
Miscellaneous Exercises #441:52
Exercise 6 and 7
Miscellaneous Exercises #538:11
Exercise 8 and 9
Miscellaneous Exercises #624:55
Exercise 10

Requirements

Empirical Probability
Theoretical or Classical Probability
Basics of Sets
Preferably all the Courses that Come Before this Course in Our Road Map

Description

In Basic High School mathematics, you'll come across three approaches to probability:

Empirical Probability
Statistical Probability (Classical Probability)
Axiomatic Approach to probability

This course teaches the axiomatic approach to probability by discussing the theory first and then using many useful typical example. In the end, you will be able to calculate the probability of almost any typical event, as long as it is not beyond the scope of this text.

This course is also a part of a road map that takes from the basics of mathematics (pre-algebra - class 6) all the way up to calculus (class 12) based on the Indian system of education (NCERT). The text used here will give you a sturdy and robust foundation in mathematics provided that the whole road map is studied from beginning to end. The road map is highly recommended if you are planning a career in science, mathematics or engineering.

To access the road map, please search for "Great IT Courses" on the internet. on the website, please read the page titled as, "Mathematics 6-12 Standard". The same page has also been linked from the second lecture of the course.

To locate this particular course in the road map, please go to the page related to "Class 11". This course is title as, "16. Probability".

Thank you!

Who this course is for:

High School Students who are looking to Understand Basic Mathematics Logically, thereby using the Acquired Knowledge in Higher Mathematics or Other Branches of Science Like Physics, Chemistry or Engineering

Axiomatic Probability - Mathematics

What you'll learn

Explore related topics

Course content

Introduction2 lectures • 5min

Definitions5 lectures • 2hr 35min

Algebra of Events5 lectures • 2hr 32min

Axiomatic Approach to Probability25 lectures • 12hr 40min

Miscellaneous Examples12 lectures • 6hr 59min

Requirements

Description

Who this course is for: