Simple and compound events

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

In statistics, an event is a collection of one or more of the outcomes of an experiment.

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.

Keep in mind that any capital letter could be used to represent an event (simple or compound)

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.

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