It is well known that the evolutionary process leads to the majority of amino acids clustering in some regions rather than being homogenously distributed along a protein. Among numerous factors affecting the evolutionary process is chance, whose impact therefore should be present in a protein primary structure. The issue of how to measure the random distribution of amino acids in a primary structure is of importance for the understanding of protein structure and functions. In this study, we use the random principle as a tool to analyze and compare the distributions of amino acids in the primary structure of the p53 protein family. The results, for example, show that the amino acids are distributed more randomly in mouse p53 and less randomly in common tree shrew p53, the distribution ranks of amino acids are relatively lower in the functional regions (about 0.5 on average) than in the whole sequences (about 1.2 on average) except for mouse p53. From the probabilistic distribution view, the composition of human p53 is relatively stable in the functional regions rather than in the whole sequence, which may suggest one of the potential effects on the mutations inducing human cancers. In general, we can use the distribution probability to present quantitatively a type of distribution of amino acids in a protein, to compare quantitatively the magnitude of clusters between different proteins and to track the effect of chance on the evolutionary process.