Simple and compound events

Before we show you the difference between simple and compound events, we will start with a definition of event.

If the event has only 1 outcome, the event is called a simple event. A simple event is usually denoted by E₁, E₂, E₃, E₄, and so forth.  Any other capital letter could be used as well.

On the other hand, if the event has at least 1 outcome, it is called a compound event.

A compound event is usually denoted by A, B, C, and so forth or A₁, A₂, A₃, and so forth.

Recall also that the sample space will show you all the outcomes of an experiment.

Consider again the experiment of tossing a coin twice.

The sample space is s = { HH, HT, TH, TT }

As you can see, this sample space has 4 outcomes.

What is a simple event for this experiment?

Since a simple event has only 1 outcome, each of the 4 outcomes is a simple event.

For example, consider the event

'Head on both tosses'

Head on both tosses =  { HH } and { HH } is a simple event.

By the same token, the event

'The first toss results in head and the second toss results in tails'  or { HT } is also a simple event.

What is a compound event for this experiment?

However, consider the event

' The first toss results in head '

The first toss results in head = { HH, HT }

This event is a compound event since there are two outcomes.

By the same token, consider the event

' The tosses result in at most 1 tail  '

The event ' The tosses result in at most 1 tail ' is the same as ' The tosses result in no tail or the tosses give exactly 1 tail '

The tosses results at most 1 tail = { HH, HT, TH }

Since this event has 3 outcomes, it is a compound event.

Hopefully the example above clearly showed the difference between simple and compound events.