What does "probability" mean in mathematics?

Probability is also called "probability". It reflects the possibility of random events. Random events refer to events that may or may not occur under the same conditions. For example, it is a random event to randomly select one from a batch of goods with genuine products and defective products, and "what is extracted is genuine products".

Suppose a random phenomenon is tested and observed n times, in which event A appears m times, that is, its frequency is m/n. After a lot of repeated experiments, m/n is often closer to a constant (see Bernoulli's law of large numbers for details). This constant is the probability of the occurrence of event A, which is usually expressed by P (A).

Extended data:

Probability type:

1, classical probability type

The object of classical probability discussion is limited to the case that all possible results of random experiments are finite and equal, that is, the basic space consists of finite elements or basic events, the number of which is recorded as n, and the possibility of each basic event is the same.

If event A contains m basic events, the probability of event A is defined as p(A)=m/n, that is, the probability of event A is equal to the number of basic events contained in event A divided by the total number of basic events in the basic space, which is the classical definition of probability by P.-S. Laplace.

Historically, classical probability was produced by studying the problems in gambling games such as dice. To calculate the classical probability, all the basic events can be listed by exhaustive method, and then the number of basic events contained in an event can be counted and divided, that is, the calculation process can be simplified by combined calculation.

2. Geometric probability

Geometric Probability If there are infinitely many basic events in the random test, and each basic event has the same possibility, then the classical probability can't be used, so the geometric probability is generated. The basic idea of geometric probability is to associate an event with a geometric region and calculate the probability of an event by using the measurement of the geometric region. Buffon's needle throwing problem is a typical example of applying geometric probability.

Let the event A (also a region in S) contain A, and its metric size is μ(A). If P(A) represents the probability of event A, considering the "uniform distribution", the probability of event A is taken as: P(A)=μ(A)/μ(S), and the calculated probability is called geometric probability. If φ is an impossible event, that is, φ is an empty area in ω, and its metric size is 0, then its probability p (φ) = 0.

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