# Probabilities of Multiple Random Experiments

In this mission of this Probability Fundamentals in R course, you’ll learn how to solve complex probability problems. You’ll learn about concepts such as set complements, the multiplication rule, independent and non-independent events, and more.

Mathematicians are known for taking complex problems and breaking them down into more approachable bits and pieces, and that’s a skill you’ve probably begun to develop while learning to code, too. Probability is no different! In this mission, you’ll take what you’ve learned in the previous missions and apply it to solve more involved probability problems.

In addition, you will learn what it means for an event to occur with and without replacement.

By the time you complete this mission, you will have learned new techniques and have answered the following probability questions:

• What is the probability that it takes three flips or more for a coin to land heads up?
• What is the probability of a coin landing heads up 18 times in a row?
• What is the probability of getting at least one 6 in four throws of a single six-sided die?
• What is the probability of getting at least one double-six in 24 throws of two six-sided dice?
• What is the probability of getting four aces in a row when drawing cards from a standard 52-card deck?

## Objectives

• Learn how to use complements to solve problems
• Learn about the multiplication rule of probability
• Learn about independent and non-independent events.

## Lesson Outline

1. Multiple Random Experiments
2. The Multiplication Rule
3. Independent Events
4. Independence vs Mutual Exclusivity
5. Complements
6. Using Complements with Probability
7. Another Application: Detecting Dependence
8. Next Steps
9. Takeaways