Go over Section 1.2 from the textbook. Pay attention to how sample spaces are described in the text. But when doing so, in a sequential experiment, think of the set of possibilities in each step. Try to think of the sample space in terms of Cartesian products of the possibilities of each step. Do you see the connection?

Compare the development in the handout with the text. You will see the text mentions events, but not the space of events explicitly.

You have the box about properties of probability laws on page 14 of the text. Do you notice that we have derived exact analogs of (a), (b) and (c) in terms of indicator functions? Can you write an analog for (d) in terms of indicator functions and prove it?