Over the next few chapters, we will explore both probability and statistics as methods of examining both data-driven situations and real-world scenarios. The rules of probability govern the basics of prediction. We use probability to define the chances of the occurrence of an event.
In this chapter, we will look at the following topics:
- What is the probability?
- The differences between the Frequentist approach and the Bayesian approach
- How to visualize probability
- How to utilize the rules of probability
- Using confusion matrices to look at the basic metrics
Probability will help us model real-life events that include a sense of randomness and chance. Over the next two chapters, we will look at the terminology behind probability theorems and how to apply them to model situations that can appear unexpectedly.
One of the most basic concepts of probability is the concept of a procedure. A procedure is an act that leads to a result, for example, throwing a die or visiting a website.
An event is a collection of the outcomes of a procedure, such as getting a head on a coin flip or leaving a website after only 4 seconds. A simple event is an outcome/event of a procedure that cannot be broken down further. For example, rolling two dice can be broken down into two simple events: rolling die 1 and rolling die 2.
The sample space of a procedure is the set of all possible simple events. For example, an experiment is performed in which a coin is flipped three times in succession. What is the size of the sample space for this experiment?
The answer is eight because the results could be any one of the possibilities in the following sample space: {HHH, HHT, HTT, HTH, TTT, TTH, THH, or THT}.