1. Random events and their relationships and operations
1. Randomized trials
(1) Can be repeated under the same conditions
(2) There may be more than one result of each test, and all possible results of the test can be specified in advance
(3) It is not possible to determine which outcome will appear before performing an experiment
2. Sample points: every possible outcome of a randomized trial
3. Sample space: the set of all sample points is called sample space
4. Events:
- Random events: A subset of the sample space is called a random event, which often attaches specific circumstances or specific conditions to the event
- Elementary event: a single point set consisting of a single sample point
- Event Occurrence: In each trial, if and only if a sample point in the result set of the event occurs, the event is said to occur.
- Necessary event: It always occurs in every trial and is called a necessary event.
- Impossible event: An event that does not occur in any trial is called an impossible event and is recorded as an empty set.
- Distinguish between mutually exclusive events and opposing events:
Mutually exclusive events mean that two events cannot occur at the same time, but neither of them can occur.
And the opposite events are not only impossible to happen at the same time, but also impossible to happen, that is, at least one of them must happen, that is, A∪B=Comprehensive
- Nature of Event Operations
Give the title of the conditions represented by letters, clarify the or and non-relationship between the conditions, use ∪ to replace or, use ∩ to replace and, use non to replace negation, and skillfully use the above operation laws
2. Probability
1. Axiomatic definition of probability
2. The nature of probability is important
3. Classical outline
(1) Definition: The sample points of an experiment are limited, and the probability of each sample point appearing is equal, then this experiment is a classical probability model (equal probability model), such as throwing dice.
(3) Geometric outline
