Defining an Elementary Event
An elementary event, in probability theory, refers to a single, indivisible outcome of a random experiment. It is the most basic result that can occur and cannot be broken down further into simpler events. When an experiment is conducted, exactly one elementary event will occur.
Characteristics of Elementary Events
Each elementary event is unique and mutually exclusive, meaning that if one elementary event occurs, no other elementary event can occur at the same time. The collection of all possible elementary events forms the sample space for the experiment. These events serve as the building blocks for all other, more complex events in probability.
Practical Example: Coin Toss and Dice Roll
Consider flipping a single coin. The elementary events are 'Heads' (H) and 'Tails' (T). For rolling a standard six-sided die, the elementary events are rolling a '1', '2', '3', '4', '5', or '6'. In both cases, each outcome is distinct and cannot be subdivided further, representing a single result from the experiment.
Importance in Probability Calculations
Understanding elementary events is crucial because probabilities of all other events are calculated by summing the probabilities of the elementary events they comprise. For instance, the event 'rolling an even number' on a die is composed of the elementary events {2, 4, 6}. If all elementary events are equally likely, the probability of any single elementary event is 1 divided by the total number of elementary events.