# Compound, Complex, Composite, Elementary, Simple, Events :: Probability

## 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:

A Composite Event : The Event of getting an even number.

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:

A Composite Event : The Event of getting a number divisible by three.

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:

A Composite Event : The Event of drawing a token with a number which is a multiple of 5.

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.

Therefore, we can say that

• Compound events can be broken down into two or more elementary events.

The compound event of getting an even number can be broken down into the events of geting 2, 4 and 6.

• The compound event occurs when any one of the elementary events making up the compound events occur.

The compound event of getting an even number is said to occurr, when any of the events of geting 2, 4, 6 occur.

## Elementary or Simple Events

Events which cannot be further sub - divided into smaller events are called elementary or simple events. It would not be possible to visualise/view other events which make up these.

### Examples

1. In the experiment of tossing a coin, following are the elementary events :

1. The Event of getting a HEAD
2. The Event of getting a TAIL

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

2. In the experiment of rolling a die, following are the elementary events :

1. The Event of getting 1 on the die.
2. The Event of getting 2 on the die.
3. ...
4. ...
5. ...
6. The Event of getting 6 on the die.

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

3. In the experiment of drawing a token from a bag containing 20 tokens numbered (in words) from 1 to 20, following are the elementary events :

• The Event of drawing a token with the number ONE on it.
• The Event of drawing a token with the number TWO on it.
• ...
• ...
• ...
• The Event of drawing a token with the number NINETEEN on it
• The Event of drawing a token with the number TWENTY on it.

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

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