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# 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.How many possible outcomes are there for this experiment?Determine if each event is compound or simple. (a) Rolling a 1 on the first die.  (b) Rolling an even number on the first die and an odd number on the second die.What is the probability of rolling an even number on the first die and an odd number on the second die? What is the probability of rolling one even number and one odd number, if it doesn't matter on which die each occurs?

#### Exercise 1

What is the set corresponding to the event "rolling an even number on a six-sided 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?