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# Applied Probability

## A framework for understanding the world around us, from sports to science.

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.

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1. 1

### Intro to Probability

Think probabilistically and explore the wide-reaching applications of probability.

1. #### Thinking Probabilistically

Use probability to avoid logical fallacies and quantify rare events.

2. #### Using Outcomes

Calculate probabilities as fractions of the total count of possible outcomes.

3. #### Applications

Explore applications of probability drawn from physics, meteorology, and tennis!

2. 2

### Probability Rules

Get the basics down.

1. Included with
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#### Rule of Sum and Rule of Product

When do you add probabilities and when do you multiply them?

2. Included with
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#### Inclusion-Exclusion

Use Venn diagrams to make deductions about probabilities.

3. Included with
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#### The Rule of Complement

Learn to simplify problems by shifting your perspective to consider the probability an event does NOT happen.

4. Included with
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#### Problem Solving

Put your probability knowledge to the test solving some real-world problems!

3. 3

### Conditional Probability

Update your assumptions with the information around you.

1. Included with
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#### Defining Conditional Probability

Explore the mathematics that governs the probabilities of dependent events.

2. Included with
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#### Applying Conditional Probability

Practice calculating conditional probabilities.

3. Included with
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#### Bayes' Theorem

How is the probability of A given B related to the probability of B given A?

4. Included with
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#### Misconceptions

Explore problems where misconceptions commonly arise, including the Monty Hall problem.

4. 4

### Probability Applications

Sports, economics, science, and more.

1. Included with
Brilliant Premium

#### The Tennis Problem

How is a player's probability of winning a point related to the probability they win the whole game?

2. Included with
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#### Probability in Science

Apply probability to solve problems in genealogy, cancer research, biology, and physics.

3. Included with
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#### Probability in Economics

Use probability and expected value to forecast financial futures.

4. Included with
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#### Probability in Quality Control

Extend what you know about probability to the understand the work potential of assembly lines.

5. 5

### Advanced Techniques

Push the frontiers of your knowledge with these probabilistic techniques.

1. Included with
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#### Geometric Probability

Use geometric reasoning to understand probability distributions of games with infinitely many outcomes.

2. Included with
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#### Bijections

Discover the surprising power of counting the same thing in two different ways!

3. Included with
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#### Recursion

Harness the power of knowing a general pattern that relates the early and late values in a sequence.

4. Included with
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#### Markov Chains

Learn what Markov chains are and use them to model the weather.