First of all, probability theory is a mathematical theory to study random phenomena, and its main concern is the possibility of events. Probability theory provides a rigorous mathematical framework for describing and analyzing the occurrence law of random events. The basic concepts of probability theory include random variables, probability distribution, expected value, variance and so on. These concepts provide a powerful tool for us to understand and calculate random events.

Statistics is a science that applies the principles and methods of probability theory to collect, process, analyze and interpret data. The main purpose of statistics is to reveal the laws and trends behind the data through statistical analysis of the data, thus providing a basis for decision-making. The basic methods of statistics include descriptive statistics, inferential statistics and hypothesis testing.

There is a close relationship between probability theory and statistics. First of all, probability theory provides a theoretical basis for statistics. Many methods and concepts in statistics are developed based on the principle of probability theory, such as sampling, estimation, hypothesis testing and so on. Secondly, statistics provides a practical application scenario for probability theory. Although probability theory provides a rigorous mathematical framework, it is difficult to verify and apply these theories without the support of actual data. Statistics makes the theory of probability theory applied and developed in practical problems by collecting and analyzing actual data.

Although probability theory is closely related to statistics, there are some differences between them. Probability theory pays more attention to the study of random phenomena themselves, and it pays attention to the possibility and law of events. Statistics pays more attention to the processing and analysis of actual data. It focuses on how to extract useful information from data and how to use this information to make decisions. In addition, probability theory usually pays more attention to the rigor and completeness of theory, while statistics pays more attention to the practicability and operability of methods.

In a word, probability theory and statistics are two interrelated and different disciplines. Probability theory provides a theoretical basis for statistics, and statistics provides a practical application scenario for probability theory. In practical application, it is necessary to flexibly use probability theory and statistics to solve practical problems according to the needs of specific problems.