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.
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.
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.
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.
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.
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.
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.