It is no long a question whether the process of evolution is affected by chance, but is to what extent. The random analysis can throw light on the underlying reasoning for the primary structure of proteins. The study on the Bcl-2 family shows that the rank per amino acid increases 93% in bovine than in chicken and rat, which indicates that the effect of chance has more impact on the evolutionary process of chicken and rat Bcl-2 and less impact on bovine Bcl-2. About one fourth of types of amino acids distribute in the highest probabilistic way in the Bcl-2 family. These phenomena are striking in four BH regions where vast majority of amino acids occur with the probabilistically simplest distribution. Mutations and variants can lead to the increased and/or decreased distribution probabilities of amino acids. Mutations 1, 2 and variant 3 target the rank increased in both affected amino acids. By contrast variants 1 and 2 lead to the rank decreased in both affected amino acids. In mutations 3 and 4, the affected amino acids change their ranks to opposite directions, i.e. the rank is lower in replaced amino acid and higher in replacing one. Using our random approaches as quantitative tools, we can measure, compare and explain the primary structures of proteins.