The first chapter the basic concepts of probability theory
1. The common concept
| class | name | definition |
| Two phenomena | OK phenomenon | Under certain conditions inevitable , called to determine the phenomenon |
| Random phenomenon | Individual test results are presented in the uncertainty, and a large number of repeat test its results but also has statistical regularity phenomenon, called a random phenomenon | |
| Randomized trial | ||
| Sample space | ||
| Sample points | ||
| Ten events | Random events | Suppose the test sample space E is S, E S of the sample space subset , referred to as random events E |
| The basic events | Of a sample point one-point set consisting of basic event called | |
| Inevitable event | Example: A = [1,2,3], B = [1,2,3,4], it is inevitable A∈B | |
| Unlikely event | Example: A = [4,5,6], B = [1,2,3,4], it is impossible A∈B | |
| Equal event | A∈B | |
| And events | A∪B, event A occurs, or at least one of B | |
| Product event | A∩B, events A, B occur simultaneously | |
| The difference incident | A-B | |
| Mutually exclusive events | A∩B = ∅, events A, B content or mutually exclusive | |
| Inverse time, the opposite event | A∪B = S and A∩B = ∅, events A, B must be a occurs, and only one occurrence | |
| De Morgan law |  |
2. Classical Probability Model
3. Conditional Probability
| name | official | Explanation |
| Multiplication formula | P（AB）=P（B|A）P（A） | P (AB) represents the probability of simultaneous events AB P (B | A) represents the probability of event B under the conditions of occurrence of an event A occurs P (A) represents the probability of event A occurs |
| Test sample space E is S, A is the event E, B . 1 , B 2 ... B n- a division of S, and P (B I )> 0, where i = 1,2 ... n, j = 1,2 ... n | ||
| Full probability formula | P（A）=P（A|B1）P（B1）+P（A|B2）P（B2）+...+P（A|B2）P（B2） | |
| Bayesian formula |  |
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