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

In statistics, an event is a collection of one or more results from an experiment.

If the event has only 1 result, the event is called a simple event. A simple event is usually denoted with E. designated1, E2, E3, E4th, and so on. Any other capital letter can also be used.

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

A compound event is usually called A, B, C, etc., or A. designated1, A2, A3, and so on.

Remember that any capital letter can be used to represent an event (simple or compound).

Also, remember that the sample room shows you all the results of an experiment.

Consider again the experiment of flipping a coin twice.

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

As you can see, this sample room has 4 results.

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

Heads on both throws = {HH} and {HH} is a simple event.

So is the event

‘The first toss is heads and the second toss is tails’ or {HT} is also a simple event.

What is a composite event for this experiment?

However, consider the event

‘The first throw is the head’

The first throw results in heads = {HH, HT}

This event is a composite event because it has two outcomes.

Also consider the event

‘The litters result in a maximum of 1 tail’

The event ‘The litters result in at most 1 tail’ is the same as ‘The litters do not result in a tail or the litters result in exactly 1 tail’

The litters result in at most 1 tail = {HH, HT, TH}

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

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