At a Glance  Compound Events
A compound event is an event that can be described in terms of simpler events, not a riot that occurs on prison grounds.
A compound event will often, but not always, involve multiple experiments. Outcomes that result from combining two experiments are written like ordered pairs:
(outcome of first experiment, outcome of second experiment)
For instance, if Dr. Frankenstein tried bringing his creation to life AND curing its acne in one fell swoop, he'd be engaging in a compound event.
Sample Problem
If we roll a die and flip a coin, the sample space is
{(1, H), (1, T), (2, H), (2, T), (3, H), (3, T), (4, H), (4, T), (5, H), (5, T), (6, H), (6, T)}.
"Rolling an even number and landing a head on the coin flip" is a compound event, since this event can be described in terms of the two simpler events "rolling an even number" and "landing a head on the coin flip."
Example 1
An experiment consists of rolling two fair dice.

Exercise 1
What is the set corresponding to the event "rolling an even number on a sixsided die and landing a head on a coin flip"?
Seems like an awfully complicated alternative to drawing straws, but okay.
Exercise 2
What is the probability of rolling an even number and landing a head on a coin flip?