1. Mathematical modeling: describe and analyze probability problems by establishing mathematical models. This method usually needs to abstract and simplify the problem in order to transform it into a form that can be expressed by mathematical formulas. Then, the mathematical tools such as probability theory and statistics are used to analyze and solve the model.

2. Random simulation: A large number of random samples are generated by computer programs to simulate the randomness of practical problems. This method can be used to solve some probability problems that are difficult to be expressed by mathematical formulas, such as Monte Carlo method and molecular dynamics simulation.

3. Statistical analysis: through the collection, collation and analysis of actual data, the probability problem is studied. This method usually needs statistical processing such as hypothesis testing and regression analysis to reveal the laws and trends behind the data.

4. Bayesian inference: According to the known prior information and observation data, the posterior probability distribution is calculated by Bayesian theorem. This method is widely used in machine learning, signal processing and other fields.

5. Markov chain: describe the dynamic process of probability problem by constructing state transition matrix. Markov chain is a discrete-time Markov process with the characteristics of "no aftereffect" and "stationarity", which can be used to solve queuing theory, network flow control and other problems.

6. combinatorial optimization: the probability problem is transformed into a combinatorial optimization problem, and then it is solved by graph theory, dynamic programming and other methods. This method is widely used in combinatorial optimization problems such as traveling salesman problem and knapsack problem.

7. Random algorithm: design an algorithm that can find the approximate solution or optimal solution of probability problems in a limited time. Random algorithms usually use randomization technology to improve the efficiency and performance of the algorithm, such as genetic algorithm and ant colony algorithm.

In a word, the research methods of probability problems are various, and the appropriate methods can be selected according to the characteristics and needs of specific problems. At the same time, these methods are often interrelated and cross-applied, so they need flexible application and comprehensive analysis in practical application.