Taking the problem of drawing lots as an example, this paper presents the basic idea and form of the total probability formula step by step through the in-depth analysis of it. In this paper, the source of event complexity is discussed to explore the search process of the complete event group in depth, and then several typical scenarios and analysis methods for determining the complete event group are discussed to help readers understand and master the total probability formula.

In this paper, the grey correlation degree analysis method in the grey system theory is applied, and the grey correlation degree is taken as the measurement index to find the possible related factors that affect the number of important scientific and technological achievements at the international advanced level in Shandong Province, and the correlation degree coefficient between the number of important scientific and technological achievements and the influencing factors is calculated to reveal the influence degree of each influencing factor. The future scientific and technological innovation and output of scientific and technological achievements in Shandong Province are analyzed.