# Events

#### Elementary Event

An elementary event is one of the elements that make up the sample space.

For example, if a die is thrown, an elementary event would be a 5.

#### Compound Event

A compound event is any subset of the sample space.

For example, if a die is thrown, a compund event would be an even number, another, a multiple of 3.

#### Sure Event

The sure event, **S**, is formed by all possible results (that is to say, the sample space).

For example, rolling a die and obtaining a score of less than 7.

#### Impossible Event

The impossible event, , does not have an element.

For example, rolling a die and obtaining a score of 7.

#### Disjoint Events or Mutually Exclusive

Two events, A and B, are mutually exclusive when they don´t have an element in common.

If outcome A is to obtain an even number from a die and B is to obtain a multiple of 5, A and B are mutually exclusive events.

#### Independent Events

Two events, A and B are independent if the probability of the succeeding event is not affected by the outcome of the preceeding event.

By rolling a die twice, the results are independent.

#### Dependent Events

Two events, A and B are dependent if the probability of the succeeding event is affected by the outcome of the preceeding event.

For example, two dependent events would be drawing two cards from a deck (one at a time) without redepositing them.

#### Complementary Event

The complementary event of **A** is another event that is realized when **A** is not realized. It is denoted by or A'.

For example, the complementary event of obtaining an even number when rolling a dice is obtaining an odd number.