Summary

In this chapter, we have primarily discussed the core ideas of probability theory, and in particular discrete probability. These allow us to calculate the probability that an event will occur, or, in other words, the chance that it will occur. We then applied these ideas to some popular modern innovations.

First, we constructed a probability space, made up of a sample space, a set of events, and a probability measure. The definition of these topics led directly to many elementary properties of probabilities and formulas to compute probabilities of events, such as those made up of unions of events and certain intersections of events. This led to an important class of probability spaces: the Laplacian space, where each outcome is equally likely. This reduces many probability calculations to counting problems, which we learned to solve in Chapter 4, Combinatorics Using SciPy.

Then, we considered conditional probability, which is essentially the idea that gaining new knowledge...