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Fat Chance

Probability from the Ground Up

Benedict Gross, Joseph Harris, and Emily Riehl

Created specifically for those who are new to the study of probability, or for those who are seeking an approachable review of core concepts prior to enrolling in a college-level statistics course, Fat Chance prioritizes the development of a mathematical mode of thought over rote memorization of terms and formulae. Through highly visual lessons and guided practice, this course explores the quantitative reasoning behind probability and the cumulative nature of mathematics by tracing probability and statistics back to a foundation in the principles of counting.

In Modules 1 and 2, you will be introduced to basic counting skills that you will build upon throughout the course. In Module 3, you will apply those skills to simple problems in probability. In Modules 4 through 6, you will explore how those ideas and techniques can be adapted to answer a greater range of probability problems. Lastly, in Module 7, you will be introduced to statistics through the notion of expected value, variance, and the normal distribution. You will see how to use these ideas to approximate probabilities in situations where it is difficult to calculate their exact values.

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What's inside

Learning objectives

An increased appreciation for, and reduced fear of, basic probability and statistics
How to solve combinatorial counting problems
How to solve problems using basic and advanced probability

An introductory understanding of the normal distribution and its many statistical applications
An ability to recognize common fallacies in probability, as well as some of the ways in which statistics are abused or simply misunderstood

An increased appreciation for, and reduced fear of, basic probability and statistics
How to solve combinatorial counting problems
How to solve problems using basic and advanced probability
An introductory understanding of the normal distribution and its many statistical applications
An ability to recognize common fallacies in probability, as well as some of the ways in which statistics are abused or simply misunderstood

Syllabus

1 Basic Counting

1.1 Counting Numbers

1.2 Large Numbers

1.3 The Multiplication Principle

1.4 More on the Multiplication Principle and Factorials

1.5 The Subtraction Principle

2 Advanced Counting

2.1 Counting Collections

2.2 Binomial Coefficients

2.3 Applications of Collections

2.4 Multinomials

2.5 Collections with Repetition

3 Basic Probability

3.1 Flipping Coins

3.2 Rolling Dice

3.3 Playing Poker

3.4 Distributions of Bridge Hands

4 Expected Value

4.1 Expected Value: Chuck-A-Luck

4.2 Expected Value: Slot Machines

4.3 Strategizing

5 Conditional Probability

5.1 The Monty Hall Problem

5.2 Conditional Probability: Set-Up and Examples

5.3 Conditional Probability: Elections

6 Bernoulli Trials

6.1 Bernoulli Trials

6.2 The Gambler's Ruin

7 The Normal Distribution

7.1 Games

7.2 Games: Examples and Variance

7.3 Iterating Games

7.4 The Normal Distribution - Part 1

7.5 The Normal Distribution - Part 2

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Explores probability and statistics through the principles of counting, making the concepts easy to grasp

Suitable for beginners with little to no prior knowledge in probability and statistics

Provides a strong foundation for students pursuing further studies in statistics or related fields

Covers a wide range of topics, including basic counting, advanced counting, basic probability, expected value, conditional probability, Bernoulli trials, and the normal distribution

Taught by instructors with expertise in mathematics and statistics

Concepts are explained clearly and concisely, making the course accessible to a broad audience

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Reviews summary

Fat chance: probability made accessible

Learners say this course is one of the best MOOCs on probability. They rave about the instructors, the videos, the examples, and the practice exercises. Students say this course is great for beginners who want to build their intuition about probability and statistics.

The video lectures are described as vivid, attractive, and engaging.

"The course materials are easy to understand, and the video lectures are vivid, attractive and really helps you understanding the concepts."

"All the three instructors are really good at their jobs, and they make math so much fun than I ever expected!"

Each practice exercise has a companion video that serves as "office hours", offering step-by-step explanations.

"I particularly liked the "office hours" feature : a video for each Practice Exercise, giving a clear step-by-step explanation of how the problem was approached and solved."

This course is highly recommended for beginners in probability & statistics.

"If you're looking for a course that starts at the very basic concepts and builds up your intuition slowly, this one is for you."

"Although I had an introductory course a few decades ago, my emphasis was on memorization and manipulation of formulas."

"So, I found this course very helpful, as it starts from the fundamental: counting numbers."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Fat Chance: Probability from the Ground Up with these activities:

Review Set Theory Concepts

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Review the basics of set theory, which provides the foundation for probability concepts like events and outcomes.

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Go over definitions of sets, subsets, and operations
Review properties and laws of set theory

Revisit Counting Principles

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Review the multiplication, subtraction, and counting principles to build a strong foundation for topics covered later in the course.

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Review multiplication principle and counting factorials
Review subtraction principle

Connect with a Probability Expert

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Reach out to individuals in your network or online communities to find a mentor who can provide guidance, support, and insights into probability concepts.

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Identify potential mentors through professional organizations or social media
Reach out and express your interest in connecting
Establish regular communication and seek their guidance on specific topics

Six other activities

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Create a Collection of Probability Resources

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Gather and organize a collection of valuable resources such as articles, videos, and simulations to supplement your learning and provide additional perspectives on probability concepts.

Browse courses on Probability

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Identify and gather relevant resources
Organize the resources into categories or topics
Create a central repository for easy access

Form a Study Group for Probability

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Join or form a study group to collaborate with peers, discuss concepts, and work through problems together to enhance your understanding.

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Find or create a study group with compatible peers
Establish regular meeting times and a study schedule
Take turns presenting concepts, solving problems, and facilitating discussions

Probability Calculations Practice

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Solve a variety of probability problems to develop fluency and strengthen your problem-solving abilities.

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Find practice problems from textbooks or online resources
Attempt to solve the problems independently
Check your solutions and identify areas where you need improvement

Solve Probability Puzzles

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Practice solving challenging probability puzzles to sharpen your problem-solving skills and deepen your understanding of probability concepts.

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Find online or textbook-based probability puzzles
Attempt to solve the puzzles using the concepts learned in the course
Review solutions and identify areas for improvement

Develop Visual Guide to Probability

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Create a visual guide that summarizes key probability concepts, helping you visualize and understand complex ideas.

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Research and gather information on probability concepts
Design a visual representation of each concept
Compile the visual representations into a coherent guide

Attend a Probability Workshop

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Participate in a workshop led by experts to gain hands-on experience with probability concepts and learn from industry professionals.

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Research and identify relevant workshops
Register and attend the workshop
Actively participate in discussions and exercises

Career center

Learners who complete Fat Chance: Probability from the Ground Up will develop knowledge and skills that may be useful to these careers:

Statistician

Statisticians collect, analyze, and interpret data. They use their knowledge of probability and statistics to draw conclusions about the world around us. This course can help statisticians build a strong foundation in probability and statistics. The course covers basic probability concepts such as counting, expected value, and conditional probability. It also introduces the normal distribution, which is widely used in statistics to model the distribution of data.

See salaries and explore the career path for Statistician

Actuary

Actuaries analyze the financial consequences of risk and uncertainty. They use mathematical and statistical skills to determine the probability of future events and to assess their financial impact. Probability is a fundamental concept in actuarial work, and this course can help build a strong foundation in the subject. The course covers basic probability concepts such as counting, expected value, and conditional probability. It also introduces the normal distribution, which is widely used in actuarial work to model the distribution of risks.

See salaries and explore the career path for Actuary

Underwriter

Underwriters assess the risk of insurance policies and determine the appropriate premiums. They use their knowledge of probability and statistics to assess the likelihood and impact of different risks. This course can help underwriters build a strong foundation in probability and statistics. The course covers basic probability concepts such as counting, expected value, and conditional probability. It also introduces the normal distribution, which is widely used in underwriting to model the distribution of risks.

See salaries and explore the career path for Underwriter

Data Analyst

Data analysts collect, clean, and analyze data to identify trends and patterns. They use their findings to make recommendations for businesses and organizations. Probability and statistics are essential skills for data analysts, and this course can help build a strong foundation in these subjects. The course covers basic probability concepts such as counting, expected value, and conditional probability. It also introduces the normal distribution, which is widely used in data analysis to model the distribution of data.

See salaries and explore the career path for Data Analyst

Financial Analyst

Financial analysts evaluate the financial performance of companies and make recommendations for investment decisions. They use their knowledge of probability and statistics to assess the risk and return of different investments. This course can help financial analysts build a strong foundation in probability and statistics. The course covers basic probability concepts such as counting, expected value, and conditional probability. It also introduces the normal distribution, which is widely used in financial analysis to model the distribution of returns.

See salaries and explore the career path for Financial Analyst

Risk Analyst

Risk analysts identify and assess the risks that organizations face. They use their knowledge of probability and statistics to quantify the likelihood and impact of different risks. This course can help risk analysts build a strong foundation in probability and statistics. The course covers basic probability concepts such as counting, expected value, and conditional probability. It also introduces the normal distribution, which is widely used in risk analysis to model the distribution of risks.

See salaries and explore the career path for Risk Analyst

Operations Research Analyst

Operations research analysts use mathematical and statistical techniques to improve the efficiency of business operations. They use their knowledge of probability and statistics to model business processes and to make recommendations for improvement. This course can help operations research analysts build a strong foundation in probability and statistics. The course covers basic probability concepts such as counting, expected value, and conditional probability. It also introduces the normal distribution, which is widely used in operations research to model the distribution of business processes.

See salaries and explore the career path for Operations Research Analyst

Quantitative Analyst

Quantitative analysts use mathematical and statistical techniques to analyze financial data and make investment decisions. They use their knowledge of probability and statistics to assess the risk and return of different investments. This course can help quantitative analysts build a strong foundation in probability and statistics. The course covers basic probability concepts such as counting, expected value, and conditional probability. It also introduces the normal distribution, which is widely used in quantitative analysis to model the distribution of returns.

See salaries and explore the career path for Quantitative Analyst

Market Researcher

Market researchers conduct surveys and collect data to understand consumer behavior. They use their knowledge of probability and statistics to design and analyze surveys and to draw conclusions about consumer behavior. This course can help market researchers build a strong foundation in probability and statistics. The course covers basic probability concepts such as counting, expected value, and conditional probability. It also introduces the normal distribution, which is widely used in marketing research to model the distribution of consumer behavior.

See salaries and explore the career path for Market Researcher

Investment Banker

Investment bankers help companies raise capital by selling stocks and bonds. They use their knowledge of probability and statistics to assess the risk and return of different investments. This course can help investment bankers build a strong foundation in probability and statistics. The course covers basic probability concepts such as counting, expected value, and conditional probability. It also introduces the normal distribution, which is widely used in investment banking to model the distribution of returns.

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Insurance Agent

Insurance agents sell insurance policies to individuals and businesses. They use their knowledge of probability and statistics to assess the risk of different events and to determine the appropriate amount of coverage. This course can help insurance agents build a strong foundation in probability and statistics. The course covers basic probability concepts such as counting, expected value, and conditional probability. It also introduces the normal distribution, which is widely used in insurance to model the distribution of claims.

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Data Engineer

Data engineers design, build, and maintain data systems. They use their knowledge of probability and statistics to ensure that data systems are reliable and efficient. This course can help data engineers build a strong foundation in probability and statistics. The course covers basic probability concepts such as counting, expected value, and conditional probability. It also introduces the normal distribution, which is widely used in data engineering to model the distribution of data.

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Machine Learning Engineer

Machine learning engineers design and develop machine learning models. They use their knowledge of probability and statistics to train and evaluate machine learning models. This course can help machine learning engineers build a strong foundation in probability and statistics. The course covers basic probability concepts such as counting, expected value, and conditional probability. It also introduces the normal distribution, which is widely used in machine learning to model the distribution of data.

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Teacher

Teachers develop and deliver lesson plans to students in a variety of settings. They use their knowledge of probability and statistics to teach students about the world around them. This course can help teachers build a strong foundation in probability and statistics. The course covers basic probability concepts such as counting, expected value, and conditional probability. It also introduces the normal distribution, which is widely used in education to model the distribution of student performance.

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Software Engineer

Software engineers design, develop, and maintain software systems. They use their knowledge of probability and statistics to ensure that software systems are reliable and efficient. This course can help software engineers build a strong foundation in probability and statistics. The course covers basic probability concepts such as counting, expected value, and conditional probability. It also introduces the normal distribution, which is widely used in software engineering to model the distribution of data.

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Reading list

We've selected 16 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Fat Chance: Probability from the Ground Up.

Mathematical Statistics with Applications

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This introductory textbook covers a wide range of topics in mathematical statistics, including probability theory, statistical inference, and regression analysis. It provides a strong foundation for further studies in statistics and is recommended for learners who want to pursue a more rigorous approach to the subject.

Mathematical Statistics with Applications

Hardcover

$$$

Mathematical Statistics with Applications

Hardcover

$$$

Mathematical Statistics with Applications

Hardcover

$$$$