Learn Probability concepts and counting techniques

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Learn how to solve probability and counting problems through this hands-on course with many quizzes and solved problems.

184 students enrolled

What Will I Learn?

- 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

Requirements

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

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.

Who 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

Compare to Other Probability Courses

Curriculum For This Course

25 Lectures

02:57:57
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ABOUT THE COURSE: WHAT WE ARE GOING TO LEARN
1 Lecture
06:36

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Course files and course final test to check for mastery
2 Lectures
00:00

Contains important data tables used for discrete probability distribution, conditional probabilities as well as a full layout of the deck of 52 cards.

Course datafiles

2 pages

Formula sheet for Probability, counting and Discrete Random variables.

5 pages

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Basic probability concepts, conditional probability and the multiplication rule.
7 Lectures
01:03:51

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.

Preview
06:41

This quiz test the understanding of some fundamental probability concepts.

Basic probability concepts

2 questions

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

Venn diagrams, Union, Intersection and complement of events

09:27

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

Writing events in probability

1 question

How to find the intersections of events in probability

Intersection of events

1 question

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.

Computing basic probabilities and explanation about the deck of 52 cards

07:26

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

Finding the complement of events

1 question

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.

Probabilty about cards being select and Addition Rule of Probability

11:07

Computing probabilities pertaining to the addition rule of probability.

Addition Rule of Probability: No. 1

1 question

Applying the concepts of the addition rule of probability.

Addition Rule of Probability: No. 2

1 question

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

Probability about Multiple choices

1 question

Using the addition rule of Probability to compute probabilities.

Addition Rule of Probability: No. 3

1 question

Calculating probabilities with the "At least one" keyword

Calculating probabilities .."At least one"

1 question

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.

Conditional probability - Multiplication rules of probability

16:51

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

Probability about two independent events

2 questions

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

Probability with independent events

1 question

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.

Solved problems: Addition and multiplicative rules of probability

10:31

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

Multiplicative rule of probability -Solved problem

01:48

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Basic Counting Techniques, Permutations and combinations concepts
4 Lectures
16:00

This lecture explains the fundamental principle of counting technique.

Fundamental principle of counting

01:58

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

Fundamental counnting N0. 1

2 questions

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

Fundamental principle of counting N0. 2

2 questions

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

How many access codes can we create without a given digit?

1 question

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

Permutation of n elements

01:54

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

Number of distinguishables ways in counting

1 question

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

Permutations with duplicates or repeated elements

02:55

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.

Permutation of n elements taken r at a time (1)

1 question

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

How many access codes can we create using permutations?

1 question

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.

Combination principles

09:13

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

Calculating combinations - No. 1

1 question

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

Calculating combinations - No. 2

1 question

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Discrete probability distributions.
10 Lectures
01:16:34

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.

Probability distribution of a discrete Random variable

12:29

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

Discrete probability distribution

1 question

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

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.

Standard deviation of a discrete random variable

1 question

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.

Binomial distribution - Part 1 -

06:50

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

Binomial distribution - Part 2 -

08:06

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

Binomial distribution - Part 3 -

12:18

This quiz computes a probability of a binomial distribution.

Binomial distribution quizzes

5 questions

The Multinomial Distribution

05:14

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.

Hypergeometric Distribution

07:40

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

How to use the Hypergeometric distribution

1 question

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.

Poisson distribution and relationship with the Binomial

08:45

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

Poisson distribution Quiz

1 question

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

The geometric distribution

05:40

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.

Geometric distribution

05:25

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.

Negative Binomial Distribution

04:07

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

Negative Binomial Distribution Quiz

1 question

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Conclusion and upcoming course
1 Lecture
07:56

What have we learn in this course?

07:56

About the Instructor