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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.

**What you'll learn**

- 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

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