## 4.1 Applied Probability

Tap into a framework for understanding the world around us, from sports to science.

Thinking Probabilistically

Using Outcomes

Applications

Rule of Sum and Rule of Product

Inclusion-Exclusion

The Rule of Complement

Problem Solving

Managing Expectations

Defining Conditional Probability

Applying Conditional Probability

Bayes' Theorem

Misconceptions

Casework

Conditional Expectations

The Tennis Problem

Probability in Science

Probability in Economics

Probability in Quality Control

Geometric Probability

Bijections

Recursion

Markov Chains

Generating Functions

### Course description

How can we accurately model the unpredictable world around us? How can we reason precisely about randomness? This course will guide you through the most important and enjoyable ideas in probability to help you cultivate a more quantitative worldview. By the end of this course, you’ll master the fundamentals of probability, and you’ll apply them to a wide array of problems, from games and sports to economics and science.

### Topics covered

- Bayes' Theorem
- Complementary Probabilities
- Conditional Probability
- Economic Applications
- Expected Value
- Inclusion-Exclusion
- Independent Events
- Markov Chains
- Probability Misconceptions
- Recursion
- Science Applications
- The Monty Hall Problem

### Prerequisites and next steps

You'll need an understanding of basic algebra, including functions. For a lighter introduction to probability, see the Casino Probability course.

### Prerequisites

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### 4.2 Hypothesis Testing

Expand your statistics toolkit, learning how to make good decisions with limited data.

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