Probability as a field works to explain our random and chaotic world. Using the basic laws of probability, we can model real-life events that involve randomness. We can use random variables to represent values that may take on several values, and we can use the probability mass or density functions to compare product lines or look at the test results.

We have seen some of the more complicated uses of probability in prediction. Using random variables and Bayes' theorem are excellent ways to assign probabilities to real-life situations. In later chapters, we will revisit Bayes' theorem and use it to create a very powerful and fast machine learning algorithm, called the Naïve Bayes algorithm. This algorithm captures the power of Bayesian thinking and applies it directly to the problem of predictive learning.

The next two chapters are focused on statistical thinking. Like probability, these chapters will use mathematical formulas to model real-world events. The main difference, however, will be the terminology we use to describe the world and the way we model different types of events. In these upcoming chapters, we will attempt to model entire populations of data points based solely on a sample.

We will revisit many concepts in probability to make sense of statistical theorems as they are closely linked, and both are important mathematical concepts in the realm of data science.