3. Probability: Randomness
Events
In general, the objective of performing a random experiment is not to simply observe the outcome, but rather to determine whether or not the outcome of the experiment fulfills a certain criterium. For example, when rolling a 6-sided die, you might want to know whether or not you rolled an even number.
In other words, the point of interest is whether or not the outcome is contained in a specific subset of the sample space. Such a subset is called an event.
Event
An event is a subset of the sample space.
Consider the random experiment of rolling a 6-sided die with sample space #\Omega = \{1,2,3,4,5,6\}#.
What are the outcomes belonging to the event #A =# 'you roll an even number'?
#A = \text{'you roll an even number'} = \{2,4,6\}#
Note that event #A# is a subset of the sample space since all elements of the event are also contained in the sample space.
