2 Exploring probability and counting

 

This chapter covers

  • Basic probabilities
  • Counting rules
  • Combinations versus permutations
  • Continuous random variables
  • Discrete random variables

Our combined purpose in this chapter and chapter 3 is to explore the fascinating world of probabilities from several different angles—from the very basics to more advanced topics like conditional probabilities. Probabilities are the cornerstone of statistical analysis and many other quantitative techniques, so it makes perfect sense to start here and paint the subject of probabilities with a broad brush before tackling more specific topics in subsequent chapters.

Probability theory is not just some mathematical abstraction; on the contrary, it is a powerful tool for making informed decisions across almost any professional field—and in our personal lives. By understanding probabilities, we can quantify uncertainty, assess risks, and make informed predictions from data. Mastering probability concepts not only establishes a solid foundation from which to approach the techniques covered in the rest of this book but also opens up a world of possibilities around analyzing data, making predictions, and drawing meaningful and actionable insights.

2.1 Basic probabilities

2.1.1 Probability types

2.1.2 Converting and measuring probabilities

2.2 Counting rules

2.2.1 Multiplication rule

2.2.2 Addition rule

2.2.3 Combinations and permutations

2.3 Continuous random variables

2.3.1 Examples

2.3.2 Probability density function

2.3.3 Cumulative distribution function

2.4 Discrete random variables

2.4.1 Examples

2.4.2 Probability mass function

2.4.3 Cumulative distribution function

Summary