Review the basics of sets, operations on sets (union, intersection, and algebra of set operations) from Section 1.1 of the textbook. This may be material you are already familiar with, but its importance cannot be understated. You have to pay attention to two things that isn’t explicitly mentioned (but used) in the text: Cartesian products and indicator functions. Please use the handout for these.

The text uses Cartesian products without definition at the top of page 5 when it talks about tuples. The sets of ordered pairs of real numbers is called \({\mathbb R}^2\) in the text. This notation comes because the set of ordered pairs of real numbers is really the Cartesian product \({\mathbb R} \times {\mathbb R}\) (hence abbreviated as \({\mathbb R}^2\)). Same for triplets. Thinking in terms of Cartesian products explicitly has lot of advantages down the line (and the book uses them too with the assumption you already know it).

In general, you may think this section is simple or high school stuff. But the true beauty of this subject is primarily because of how deep even such basic stuff can be developed, and can yield so many astonishing conclusions. It is not for nothing that mathematics is often called the queen of all arts in much of the world (except in the United States, where we are taught implicitly or explicitly to look down on it as a tool or to fear it as if it were Sauron). But no longer. Probability theory is one area in math whose stunning beauty compares with the rarest of human accomplishments in any endeavor. You will get a preview of these things in this course among the experiences, and there is a lifetime of things to be explored starting from there.