Types of Events
An elementary event is every one of the elements which forms the sample space.
For example, if a die is thrown, an elementary event would be a 4.
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 or a multiple of 3.
The sure event, S, is formed by all possible results of the sample space.
For example, rolling two dice and obtaining a score of less than 13.
The impossible event, , does not have an element.
For example, rolling a die and obtaining a score of 7.
Disjoint or Mutually Exclusive Events
Two events, A and B, are disjointed or 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 (one at a time) without returning them to the deck.
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 die is obtaining an odd number.