Events and event space

Probability is the chance of a random event happening. An event A is a set (or group) of possible outcomes of an uncertain process e.g. {Heads in a single coin toss}, {rain}, {no rain}, { $T>20^\circ C$}, { $10^\circ\leq T < 20^\circ C$}. Events can be elementary (indivisible) or compound e.g. {Heads in a single coin toss} (elementary), {One head and one tail in 2 coin tosses} (compound). The set of ALL possible elementary events defines event space (sample space), which sometimes can be represented visually by using an Euler (or Venn) diagram. Figure 3.1 shows the event space for two events $\{A_1,A_2\}$. As an example, $\{A_1\}$ could be the event ``precipitating cloud'' and $\{A_2\}$ could be the event ``boundary layer below freezing''. In order to get snow falling on the ground, it is necessary that both events occur at the same time (the intersection region).

Figure: Euler diagram showing event space for 2 events.