Probabilistic Preliminaries

We consider experiments which have only a finite number of possible outcomes. We call the set of all possible outcomes, the sample space and denote Ω. For example, our experiment may consist of rolling a six sided die and examining the top face, in which case Ω. = {1, 2, 3, 4, 5, 6}. Alternatively, our experiment may consist of flipping a coin three times in a row, then Ω = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} where H stands for heads and T for tails. The reader probably has an intuitive notion of what an event is, which corresponds to this word’s use in everyday language. Formally, an event is a subset A of Ω. For example, we identify the event that the die roll is odd with the subset ({1, 3, 5}). Similarly, the event that the coin landed the same way up every time is the set ({HHH, TTT}).