DOI: https://doi.org/10.61957/joerai-20230314

Title: Student-Centered and Inquiry-based Teaching on Real Case

Author: Xiaoli Ma, Lili Zhang

Abstract

The Rule of total probability is an important formula in the probability theory and mathematical statistics, which provides an effective way to calculate complex probability problems in practical application, and often simplifies a complex probability calculation problem. However, in teaching, the application of the rule of total probability is a difficult point, because it is always difficult for students to master the analysis of complex problems, and they cannot divide the sample space well and find a suitable complete set of events, which makes it difficult to solve specific complex probability problems. This paper discusses a teaching design and executing process of the rule of total probability in probability and statistics course. This design fully demonstrates the student-centered principle. By introducing some interesting real cases the teacher proposes some questions, and then the students study the rule of total probability in a inquiry mode from the elementary to the profound. And to extend it which make use of the probability density function, and analyzing its extensive applications in insurance. This case-based inquiry teaching method, student-centered and case-driven, can fully mobilize students' learning interest and initiative, cultivate students' spirit of independent thinking and teamwork, and improve students' comprehensive application ability.