# Composite or Compound Events

Events which can be further sub-divided into (or viewed in the form of) smaller events are called composite events or compound events.

These events can be viewed as a union of two or more smaller events.

## Examples

1. In the experiment of throwing a die:

The Event of getting an even number is a Composite Event

This event can be further sub-divided or broken down into 3 simpler events

1. the event of getting 2,
2. the event of getting 4 and
3. the event of getting 6

Occurrence of any one of these events

⇒ Occurrence of the event of getting an even number.

2. In the experiment of throwing a die:

The Event of getting a number divisible by three is a composite event

This event can be further sub-divided or broken down into two simpler events,

1. the event of getting 3 and
2. the event of getting 6

Occurrence of any one of these events

⇒ Occurrence of the event of getting a number divisible by 3.

3. In the experiment of drawing a token from a bag containing 20 tokens numbered from 1 to 20:

The Event of drawing a token with a number which is a multiple of 5 is a composite event

This event can be further sub-divided or broken down into 4 simpler events,

1. the event of drawing a token with the number 5 on it
2. the event of drawing a token with the number 10 on it
3. the event of drawing a token with the number 15 on it and
4. the event of drawing a token with the number 20 on it

Occurrence of any one of these events

⇒ Occurrence of the event of drawing a token with a number which is a multiple of 5.

# Elementary or Simple Events

Events which cannot be further sub - divided into smaller events are called elementary or simple events.

## Examples

1. In the experiment of tossing a coin:

1. The Event of getting a HEAD is an Elementary Event

This event cannot be further sub-divided or broken down into simpler events.

2. The Event of getting a TAIL is an Elementary Event

This event cannot be further sub-divided or broken down into simpler events.

2. In the experiment of rolling a die:

1. The Event of getting ONE on the die is an Elementary Event.

2. The Event of getting TWO on the die is an Elementary Event.

3. ...
4. ...
5. ...
6. The Event of getting SIX on the die is an Elementary Event.

3. In the experiment of drawing a token from a bag containing 20 tokens numbered from 1 to 20:

1. The Event of drawing a token with the number ONE on it is an Elementary Event.

2. The Event of drawing a token with the number TWO on it is an Elementary Event.

3. ...
4. ...
5. ...
6. The Event of drawing a token with the number NINE TEEN on it is an Elementary Event.

7. The Event of drawing a token with the number TWENTY on it is an Elementary Event.

Therefore, we can say that compound events can be broken down into two or more elementary events. The compound event occurs when any one of these elementary events occur.