First of all, it is clear that probability is defined in the form of axioms in mathematics. The definitions of probability statistics, classical probability and geometric probability in various textbooks are all descriptive. Teachers should not try too hard to figure out and explore the language there, but should understand its essence. It is not difficult to generalize the concept of probability, but if we discuss it theoretically or philosophically, there will be a lot of problems that need not be discussed in middle school (or even university) mathematics courses. Here, I want to talk about some views on' definition' in mathematics. We don't want to talk about the necessity, function and significance of giving a definition in mathematics. Every math teacher knows this. What we want to talk about is the opposite side, which is also where we think there are some problems, that is, excessive pursuit of definition, excessive exploration of the words in the book, and neglect of the grasp of the overall spirit. To define any concept, you need to use some words. Strictly speaking, these words still need to be defined. Other words are needed to define these words. Therefore, this is an infinitely upward task, and it cannot be completed unless it stops somewhere. In other words, there must be some undefined words as the starting point of discussion. This point is put forward in the hope that people will not be superstitious about definitions. Some people think that things that are not defined are not strict, and only when they are defined are they strict. This view is not comprehensive. Secondly, some definitions, if any, are unnecessary for many people. Most scientists don't need to know the theory of real numbers (the strict definition of real numbers), and most mathematicians don't need to master the definition of natural numbers given by Piano's axiom. Although strict expression is very important, the most important vitality of mathematics comes from its problems and ideas, from people's exploration, guess and analysis. The statistical definition of probability can usually be described as follows: under the same conditions, a large number of repeated experiments are done, and the ratio of the number of times k of an event to the total number of experiments n is called the frequency of this event in these n experiments. When the number of tests n is large, the frequency will be "stable" around a constant. The larger n is, the less likely the frequency will deviate from this constant. This constant is called the probability of an event. We should be clear that the above definition is only descriptive. In fact, there is a suspicion of circular definition. Because' possibility' appears in the definition. This refers to probability. (Similarly,' equal probability' usually appears in the classical definition of probability). You can try to avoid such words, but its essential meaning is unavoidable. Some people explore the definition of words such as "experiment". In fact,' doing experiments' is not difficult to understand. For example, toss a coin, touch three red balls, take ten products, and so on. Individual complex experiments are not difficult to explain to students. It is even more difficult to understand that' doing an experiment' is defined as' realizing a condition'. What is a "condition"? What is' realization'? This is obviously inappropriate. Besides,' experiment' is not a mathematical term at all.