In the chapter on probability in high school, we learned about the concept of random events . The related concepts of random events will be further discussed below.
In randomized trials, in addition to being concerned about the results of the randomized trial itself, people are often also concerned about whether the results of the trial have certain observable characteristics. In probability theory, we call the outcome of a random experiment with certain observable characteristics an event. Events can be divided into the following three categories:
(1) Random events: events that may or may not occur in a random experiment. Random events are usually represented by letters , , , etc.
For example, in the experiment of throwing a dice (six sides) , use to represent the event that " the number of points is an odd number " , then is a random event.
(2) Necessary events : Events that must occur in every trial are represented by the letter (or ) .
For example , in the above dice throwing experiment, " the number is less than " is an inevitable event.
(3) Impossible event : An event that is impossible to occur in any experiment is represented by the empty set symbol .
For example , in the dice rolling experiment above, " the number is " is an impossible event.
Obviously, inevitable events and impossible events are both deterministic events. For the convenience of discussion, they will be regarded as two special random events in the future, and random events will be referred to as events for short .