Learn Probability concepts and counting techniques

Learn how to solve probability and counting problems through this hands-on course with many quizzes and solved problems.
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155 students enrolled
Instructed by Luc Zio Academics / Math & Science
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  • Lectures 25
  • Length 3 hours
  • Skill Level Beginner Level
  • Languages English
  • Includes Lifetime access
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    Available on iOS and Android
    Certificate of Completion
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About This Course

Published 10/2013 English

Course Description

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 hands-on 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.

What are the requirements?

  • General knowledge of descriptive statistics, basic algebra
  • A strong desire to learn probability concepts.

What am I going to get from this course?

  • By the end of this course you will understand probability concepts and be able to solve commons probability problems
  • By the end of this course, you will be able to compute conditional probabilities
  • By the end of this course, you will be able to understand how to solve probability problems using the addition and multiplicative rules.
  • By the end of this course, you will be able to solve basic counting problems using permutations and combinations formulas
  • By the end of this course, you will be able to compute probabilities using the Poisson distribution
  • By the end of this course, you will be able to compute probabilities using the Binomial distribution
  • By the end of this course you will understand how to solve problems using the Hypergeometric distribution
  • By the end of this course, you will be able to compute probabilities using the multinomial distribution
  • By the end of this course, you will be able to compute probabilities using the Geometric and Negative Binomial (or Pascal) distribution

What is the target audience?

  • College students, programmers and anyone interested in understanding probablity
  • People studying liberal arts, law and any other field where critical reasoning and logical thinking is very important
  • Anyone interested in understanding basic probability theory

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

Section 1: ABOUT THE COURSE: WHAT WE ARE GOING TO LEARN
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
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.

Formula sheet for Probability, counting and Discrete Random variables.
5 pages
Section 3: Basic probability concepts, conditional probability and the multiplication rule.
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.

2 questions

This quiz test the understanding of some fundamental probability concepts.

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.

1 question

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

1 question

How to find the intersections of events in probability

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.

1 question

Purpose of this quiz is to find the complement of an event

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.

1 question

Computing probabilities pertaining to the addition rule of probability.

1 question

Applying the concepts of the addition rule of probability.

1 question

This quiz demonstrate how to compute probabilities in multiple choice questions.

1 question

Using the addition rule of Probability to compute probabilities.

1 question

Calculating probabilities with the "At least one" keyword

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.

2 questions

This quiz demonstrate how to compute the probability for two independent events.

1 question

This quiz shows how to compute probability when the events are independents.

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.

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
01:58

This lecture explains the fundamental principle of counting technique.

2 questions

This quiz illustrates the fundamental counting principle, how to use it to solve problems

2 questions

This quiz demonstrate how to apply the fundamental counting principle to data.

1 question

This quiz uses the principles of permutations and couting to solve real world problems.

01:54

This lecture explains how to compute simple permutations of n elements using the factorial formula.

1 question

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

02:55

This lecture deals with the number of permutations where certain elements are duplicated or repeated.

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.

1 question

This quiz demonstrates how to use counting principles to solve practical problems.

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.

1 question

This quiz shows how to use the combination principle to calculate the number of combinations.

1 question

This quiz illustrates how to use combinations in solving real world problems.

Section 5: Discrete probability distributions.
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.

1 question

This quiz helps to understand how to calculate probabilities from a probability distribution table

1 question

In this exercise, we compute the expected value or mean of the discrete random variable

1 question

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

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.
The student can identify a binomial distribution problem after following this lecture.

08:06

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

12:18

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


5 questions

This quiz computes a probability of a binomial distribution.

The Multinomial Distribution
05:14
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.

1 question

This quiz illustrate how to use the hypergeometric distribution to calculate probabilities.

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.

1 question

This quiz demonstrates how to compute a probability using the Poisson distribution.

05:40

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

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.

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.

1 question

This quiz demonstrate how to calculate probabilities using the negative binomial distribution

Section 6: Conclusion and upcoming course
What have we learn in this course?
07:56

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Instructor Biography

Luc Zio, Adjunct faculty of Math and Statistics

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 hands-on experience with Statistics.

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