Learn Probability concepts and counting techniques
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This course covers the fundamental concepts of probability, basic counting and discrete random variables as taught in a first year introductory basic statistics class in colleges.
It is intended to students who want to learn at their own space or supplement a course note. It is also intended to anyone who wants to understand the concepts of probability through handson carefully selected problems that explain in plain English the concepts.
This class is a result of many years of teaching college level introductory statistics courses and it designed to help students understand probability concepts and especially to pay attention to the technical English language and the logic of probability.
Whether you are trying to pass an Introductory statistic course or you want to understand probability concepts, this is the course for you. It is a must for everyone especially people aspiring to programming careers, nursing, business, and especially to fields where logical thinking is important.
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Section 1: ABOUT THE COURSE: WHAT WE ARE GOING TO LEARN  

Lecture 1 
What we are going to learn in Probability and counting techniques
Preview

06:36  
Section 2: Course files and course final test to check for mastery  
Lecture 2  2 pages  
Contains important data tables used for discrete probability distribution, conditional probabilities as well as a full layout of the deck of 52 cards. 

Lecture 3 
Formula sheet for Probability, counting and Discrete Random variables.

5 pages  
Section 3: Basic probability concepts, conditional probability and the multiplication rule.  
Lecture 4  06:41  
In this lecture, we cover detailed explanations about the concept of a sample space in probability, sample points and events. These concepts are essential for solving probability problems. 

Quiz 1  2 questions  
This quiz test the understanding of some fundamental probability concepts. 

Lecture 5  09:27  
In this video, we discuss Venn diagrams, the Union of events, the intersection of Events. Many examples are provided to fully illustrate the concepts. 

Quiz 2  1 question  
Demonstrate your understanding of probability events and how to pay attention to key words in probably. 

Quiz 3  1 question  
How to find the intersections of events in probability 

Lecture 6  07:26  
In this lecture, we provide the definition of a probability using the relative frequency approach. Several examples about computing probabilities based on dices being rolled or coins being tossed are given. We conclude the video by showing all the cards in a deck of 52 cards and discuss at length the composition of the deck which is important for computing probabilities about cards being drawn from a deck of 52 cards. 

Quiz 4  1 question  
Purpose of this quiz is to find the complement of an event 

Lecture 7  11:07  
In this video, we discuss the computation of basic probability about cards being selected from a deck of 52 cards. We discuss the addition rule of probability and solve related problems to ensure that the concept is well understood. 

Quiz 5  1 question  
Computing probabilities pertaining to the addition rule of probability. 

Quiz 6  1 question  
Applying the concepts of the addition rule of probability. 

Quiz 7  1 question  
This quiz demonstrate how to compute probabilities in multiple choice questions. 

Quiz 8  1 question  
Using the addition rule of Probability to compute probabilities. 

Quiz 9  1 question  
Calculating probabilities with the "At least one" keyword 

Lecture 8  16:51  
In this lecture, we cover the concept of conditional probability and Independent events. Solved problems are presented to explain in details how to solve conditional probabilities. We also cover the multiplication rule of probability and explain the concept with examples. 

Quiz 10  2 questions  
This quiz demonstrate how to compute the probability for two independent events. 

Quiz 11  1 question  
This quiz shows how to compute probability when the events are independents. 

Lecture 9  10:31  
In this video, we illustrate through practical problems how to apply the addition rule of probability. We also demonstrate how to compute probabilities using the multiplicative rule. 

Lecture 10  01:48  
In this lecture, we illustrate how to compute probabilities when cards are selected with and without replacement using the multiplicative rule of probabilities. 

Section 4: Basic Counting Techniques, Permutations and combinations concepts  
Lecture 11  01:58  
This lecture explains the fundamental principle of counting technique. 

Quiz 12  2 questions  
This quiz illustrates the fundamental counting principle, how to use it to solve problems 

Quiz 13  2 questions  
This quiz demonstrate how to apply the fundamental counting principle to data. 

Quiz 14  1 question  
This quiz uses the principles of permutations and couting to solve real world problems. 

Lecture 12  01:54  
This lecture explains how to compute simple permutations of n elements using the factorial formula. 

Quiz 15  1 question  
This quiz demonstrates how to use the number of distinguishable permutations in solving real world problems. 

Lecture 13  02:55  
This lecture deals with the number of permutations where certain elements are duplicated or repeated. 

Quiz 16  1 question  
This quiz shows how to use the permutation or n elements taken r at a time or arrangement formula to calculate the number of permutations. 

Quiz 17  1 question  
This quiz demonstrates how to use counting principles to solve practical problems. 

Lecture 14  09:13  
In this video, we show how to compute the combination of n elements taken r at a time. Various exercises are solved in order to show in details how to calculate the number of combinations and how they are in practice to solve probability problems. 

Quiz 18  1 question  
This quiz shows how to use the combination principle to calculate the number of combinations. 

Quiz 19  1 question  
This quiz illustrates how to use combinations in solving real world problems. 

Section 5: Discrete probability distributions.  
Lecture 15  12:29  
In this video, we talk about discrete random variables and the probability distribution of discrete random variable. We explain the conditions that must be satisfied for a probability distribution to be valid. In addition, we cover the concepts of the expected value of discrete random variables, the variance and standard deviation of the discrete random variable. 

Quiz 20  1 question  
This quiz helps to understand how to calculate probabilities from a probability distribution table 

Quiz 21  1 question  
In this exercise, we compute the expected value or mean of the discrete random variable 

Quiz 22  1 question  
In this quiz, we compute the standard deviation of the discrete random variable measuring the number of homes runs. 

Lecture 16  06:50  
In this lecture, we talk about the Binomial distribution experiment an introduce important concepts about the distribution such as the failure and success probability, dichotomous outcomes and independent events. 

Lecture 17  08:06  
In this video, we present the Binomial Distribution formula and discuss shortcuts that are commonly used when solving Binomial distributions problems. 

Lecture 18  12:18  
In this lecture, we solve some Binomial distributions problems and illustrate how to use the distribution in practice. 

Quiz 23  5 questions  
This quiz computes a probability of a binomial distribution. 

Lecture 19 
The Multinomial Distribution

05:14  
Lecture 20  07:40  
This lecture illustrates how to compute probabilities using the Hypergeometric distribution. We show the differences between the Binomial distribution and the Hypergeometric distribution and use a practical example to explain how the distribution is used in solving probabilities. 

Quiz 24  1 question  
This quiz illustrate how to use the hypergeometric distribution to calculate probabilities. 

Lecture 21  08:45  
We explain the Poisson distribution concepts and illustrate the computation of probabilities using the Poisson distribution with practical examples. We also show how the Poisson distribution can be used to approximate a Binomial distribution. 

Quiz 25  1 question  
This quiz demonstrates how to compute a probability using the Poisson distribution. 

Lecture 22  05:40  
In this lecture we talk about the geometric distribution, a distribution that measures the number of trials until the first success. 

Lecture 23  05:25  
This lecture explains the Geometric distribution which models the number of failures until the first success. Solved problems are used to illustrate how the Geometric probability distribution is used to solve problems. 

Lecture 24  04:07  
We explain in detail The Negative Binomial distribution which is a discrete probability distribution that measures the number of failures until the rth success , where r >= 1. When r = 1, the Negative Binomial is the same as the geometric distribution. Exercises are used to explain how in practice the Negative Binomial distribution. 

Quiz 26  1 question  
This quiz demonstrate how to calculate probabilities using the negative binomial distribution 

Section 6: Conclusion and upcoming course  
Lecture 25 
What have we learn in this course?

07:56 
I have over 18 years of work experience in the field of statistics as an Applied Statistician. For the last twelve years, I have also been teaching undergraduate college level statistics courses at St Petersburg College. As an Applied Statistician, I have developed over the years a strong interest in using EXCEL as a statistical tool with my classes in order to give to the students real world handson experience with Statistics.