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Counting Principle

http://www.regentsprep.org/regents/math/algebra/APR1/PracCnt.htm

Permutation

http://www.regentsprep.org/regents/math/algebra/APR2/PracPerm.htm

Sample Space

http://www.regentsprep.org/regents/math/algebra/apr4/PracSamp.htm

Tree Diagrams

http://www.regentsprep.org/regents/math/algebra/apr4/practre.htm

Events (e.g. mutually exclusive events, independent events,  complements of events)

http://www.regentsprep.org/regents/math/algebra/APR6/PracMut.htm

Conditional Probability

http://www.regentsprep.org/regents/math/algebra/APR3/PracCond.htm

Probability Involving
AND and OR

http://www.regentsprep.org/regents/math/algebra/APR8/PracAND.htm

Probability of Two Events

http://www.cimt.org.uk/projects/mepres/book9/bk9i6/bk9_6i3.html

Contingency tables

http://www.everythingmaths.co.za/maths/grade-11/10-probability/10-probability-05.cnxmlplus

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https://www.mathsisfun.com/combinatorics/combinations-permutations-calculator.html

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Example Application of Bayes' Theorem: Identify Spam e-mail

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Example Application of Bayes' Theorem: Identify Spam e-mail

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https://en.wikipedia.org/wiki/Naive_Bayes_spam_filtering

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How to know if two events are Independent?

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How to know if two events are Independent?

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https://padlet.com/mmuvictor/DPS5018_main

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Advanced Application of Topic 4: Bayesian Network

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Advanced Application of Topic 4: Bayesian Network

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http://www.cs.ubc.ca/~murphyk/Bayes/bnintro.html

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Trim 3, 2015/2016

Q3a, Q3b

Trim 2, 2015/2016

Section A:

Q12, Q13, Q14

Section B:

Q2

Trim 2, 2014/2015

Section A:

Q9

Section C:

Q2b

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How to use Tree Diagram to compute conditional probabilities

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How to use Tree Diagram to compute conditional probabilities

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The following topics are covered in this notes:
4.1) Probability Basics
4.2) Sample Space, Events, and Sets

4.3) Properties of Probability
4.4) Tree Diagram
4.5) Venn Diagram
4.6) Conditional Probability
4.7) Bayes' Theorem

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http://mathbitsnotebook.com/Algebra1/StatisticsReg/ST2TwoWayTable.html

http://stattrek.com/statistics/two-way-table.aspx?Tutorial=AP

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http://passyworldofmathematics.com/three-circle-venn-diagrams/

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Bayes' theorem

https://en.wikipedia.org/wiki/Bayes%27_theorem#Derivation

https://proofwiki.org/wiki/Bayes%27_Theorem

Law of total probability

https://en.wikipedia.org/wiki/Law_of_total_probability

https://proofwiki.org/wiki/Total_Probability_Theorem

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Example Application of Bayes' Theorem: Medical diagnosis

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Example Application of Bayes' Theorem: Medical diagnosis

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Beginner Level

https://www.math.hmc.edu/funfacts/ffiles/30002.6.shtml

Advanced Level

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.690.1495&rep=rep1&type=pdf

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Advanced Application of Bayes' Theorem: Naive Bayes Classifier in Machine Learning

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Advanced Application of Bayes' Theorem: Naive Bayes Classifier in Machine Learning

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Example is in Page 11 to 13 of the attached file.

For more examples, feel free to check out:

https://en.wikipedia.org/wiki/Naive_Bayes_classifier#Examples

For more information, feel free to check out:

http://www.cs.ucr.edu/~eamonn/CE/Bayesian%20Classification%20withInsect_examples.pdf

https://www.analyticsvidhya.com/blog/2015/09/naive-bayes-explained/

https://engineering.purdue.edu/kak/Tutorials/Trinity.pdf

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The following topics are covered in this notes:
4.1) Probability Basics
4.2) Sample Space, Events, and Sets

4.3) Properties of Probability
4.5) Venn Diagram
4.6) Conditional Probability

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Attached are the solutions for "final 1416.pdf" and "final 1516.pdf"

Detailed explanation for Q2a can be found at:

https://padlet.com/mmuvictor/DPS5018_topic_4/wish/118607995

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Detailed explanation for Q3 can be found at:

https://padlet.com/mmuvictor/DPS5018_topic_4/wish/118404147

Detailed explanation for Q5 can be found at:

https://padlet.com/mmuvictor/DPS5018_topic_5/wish/118316521

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Attached are the solutions for "final 1516.pdf"

More explanation for Q9 can be found at:

https://padlet.com/mmuvictor/DPS5018_topic_4/wish/118749727

More explanation about "independent events" can be found at:

https://padlet.com/mmuvictor/DPS5018_topic_4/wish/119031463

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4.1) Probability

https://www.mathsisfun.com/data/probability.html

4.1) The Basic Counting Principle

https://www.mathsisfun.com/data/basic-counting-principle.html

4.1) Combinations and Permutations

https://www.mathsisfun.com/combinatorics/combinations-permutations.html

4.2) Complement of an Event

https://www.mathsisfun.com/data/probability-complement.html

4.2) Types of Events

https://www.mathsisfun.com/data/probability-events-types.html

4.2) Independant Events

https://www.mathsisfun.com/data/probability-events-independent.html

4.2) Dependant Events

https://www.mathsisfun.com/data/probability-events-conditional.html

4.2) Mutually Exclusive Events

https://www.mathsisfun.com/data/probability-events-mutually-exclusive.html

4.4) Probability Tree Diagrams

https://www.mathsisfun.com/data/probability-tree-diagrams.html

4.7) False Positives and False Negatives

https://www.mathsisfun.com/data/probability-false-negatives-positives.html

4.7) Bayes' Theorem

https://www.mathsisfun.com/data/bayes-theorem.html

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All Topic 4 concepts can be found in Chapter 1 to Chapter 10 of:

http://www.intmath.com/counting-probability/counting-probability-intro.php

The advantage of this website is that it contains many examples and solutions related to Topic 4; in case you want more practice problems while preparing for your MMU exams

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Summarized and Detailed Notes for Week 7 Lecture

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Summarized and Detailed Notes for Week 7 Lecture

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The following topics are covered in this notes:
4.1) Probability Basics
4.2) Sample Space, Events, and Sets
4.3) Properties of Probability
4.4) Tree Diagram
5.1) Discrete Random Variable
5.2) The Mean of a Discrete Random Variable

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This video helps explain what I was doing during Week 7 Lecture (above) and a few of my previous classes :p

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Conrad Wolfram: Teaching kids real math with computers

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4.2 to 4.3) Sample Space, Events and Probability

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4.2 to 4.3) Sample Space, Events and Probability

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http://www.math.uiuc.edu/~kkirkpat/SampleSpace.pdf

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Example Application of Topic 4: Analyzing the probability of drawing certain cards from a deck

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Example Application of Topic 4: Analyzing the probability of drawing certain cards from a deck

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Summarized and Detailed Notes for Week 7 Tutorial

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Summarized and Detailed Notes for Week 7 Tutorial

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The following topics are covered in this notes:
4.1) Probability Basics
4.2) Sample Space, Events, and Sets
4.3) Properties of Probability
4.4) Tree Diagram
5.1) Discrete Random Variable
5.2) The Mean of a Discrete Random Variable

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27 Videos on Probability and combinatorics

https://www.youtube.com/playlist?list=PLU5aQXLWR3_wDJi9fDQar3GQVfZD4SlbX

29 Videos on Independent and dependent events

https://www.youtube.com/playlist?list=PLU5aQXLWR3_x1bjE2rbvRn8sse81AUYZk

19 Videos on Random variables and probability distributions

https://www.youtube.com/playlist?list=PLU5aQXLWR3_xDN0M2ZeZ_zHIia0e42_3O

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Advanced Application of Contingency Tables: Comparing 2D Histograms using Chi Square Distribution

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Advanced Application of Contingency Tables: Comparing 2D Histograms using Chi Square Distribution

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Lesson 1) What is Chi Square Distribution

http://onlinestatbook.com/2/chi_square/distributionM.html

Lesson 2) How to compare 1D Histograms

http://onlinestatbook.com/2/chi_square/one-wayM.html

Lesson 3) How to compare 2D Histograms

http://onlinestatbook.com/2/chi_square/contingencyM.html

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4.1a) Introduction to Probability

http://onlinestatbook.com/2/probability/probability_introM.html

4.1b) Basic Concepts of Probability

http://onlinestatbook.com/2/probability/basicM.html

4.2a) Sample Space

https://www.youtube.com/watch?v=PR-A3UAO7_0

4.2b) Sample Space of Example Vacation

https://www.youtube.com/watch?v=6zWPgvEMVlE

4.2c) Sample Space of Two Dice

https://www.youtube.com/watch?v=O4Qnsubo2tg

4.2d) Sample Space of Two Dice using a Contingency Table

https://www.youtube.com/watch?v=2XToWi9j0Tk

4.3a) Addition rule for probability

https://www.youtube.com/watch?v=QE2uR6Z-NcU

4.3b) Compound probability of independent events

https://www.youtube.com/watch?v=xSc4oLA9e8o

4.3c) Various Properties of Probability using coin flipping as an example

https://www.youtube.com/watch?v=mkyZ45KQYi4

4.3d) Probability without equally likely events

https://www.youtube.com/watch?v=RI874OSJp1U&feature=youtu.be

4.3e) Permutations and Combinations

http://onlinestatbook.com/2/probability/permutationsM.html

4.3f) Permutations and Combinations using coin flipping as an example (part 1)

https://www.youtube.com/watch?v=8TIben0bJpU

4.3g) Permutations and Combinations using coin flipping as an example (part 2)

https://www.youtube.com/watch?v=udG9KhNMKJw

4.4a) Count outcomes using tree diagram

https://www.youtube.com/watch?v=Zxvc6iPKdec

4.4b) Tree Diagram Example #1

https://www.youtube.com/watch?v=6E_NVnboMB8

4.4c) Tree Diagram Example #2

https://www.youtube.com/watch?v=xf3vfczoCho

4.4d) Tree Diagram Example #3

https://www.youtube.com/watch?v=xPUm5SUVzTE

4.4e) Tree Diagram Example #4

https://www.youtube.com/watch?v=7BkcNLOf56w

4.5) Probability with playing cards and Venn diagrams

https://www.youtube.com/watch?v=obZzOq_wSCg

4.6a) Calculating Conditional Probability

https://www.youtube.com/watch?v=6xPkG2pA-TU

4.6b) Analyzing event probability for independence

https://www.youtube.com/watch?v=R-NeYKSEqns

4.6c) Conditional probability explained visually using Tree Diagram

https://www.youtube.com/watch?v=Zxm4Xxvzohk

4.7a) Introduction to Bayes' Theorem

https://www.youtube.com/watch?v=E2pOJwSwWDk

4.7b) Introduction to Bayes' Theorem for medical diagnosis

https://www.youtube.com/watch?v=OqmJhPQYRc8

4.7c) Bayes' Theorem Example for medical diagnosis

http://onlinestatbook.com/2/probability/base_ratesM.html

4.7d) Bayes' Theorem Example #2

https://www.youtube.com/watch?v=2Df1sDAyRvQ

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final 1415.pdf

Section C:

Q2a, Q2b

final 1516.pdf

Section A:

Q5, Q6, Q9, Q10, Q11

Section B:

Q2a, Q2b, Q2c, Q2d

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Post good learning materials over here to get your Bonus Marks :)

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These are what you need to know about Topic 4

Set and Probability

4.1) Probability Basics

4.2) Sample Space, Events, and Sets

4.3) Properties of Probability

4.4) Tree Diagram

4.5) Venn Diagram

4.6) Conditional Probability

4.7) Bayes' Theorem