Events — Simple and Compound

An event is any subset of the sample space $S$ — that is, any collection of outcomes we are specifically interested in. An event is said to "occur" whenever the actual result of the experiment happens to be one of the outcomes belonging to that subset.

Events are classified by HOW MANY sample points they contain:

• A simple event (also called an elementary event) is an event containing exactly one sample point. Example: on a single die roll, "getting a 4" $= \{4\}$ is a simple event, since only one outcome satisfies it.
• A compound event is an event containing two or more sample points — it is formed by combining two or more simple events together. Example: on a single die roll, "getting an even number" $= \{2, 4, 6\}$ is a compound event, since it is really three simple events ("getting a 2", "getting a 4", "getting a 6") combined into one event.

A card-deck illustration of the same distinction: drawing "the king of hearts" specifically is a simple event (exactly one card in the deck satisfies it), but drawing "a king" (any of the four kings, across all four suits) is a compound event with 4 sample points, and drawing "a face card" (any Jack, Queen, or King, across all 4 suits — $3 \times 4 = 12$ cards in total) is a compound event with 12 sample points.