Ionization of amino acids (AA) is very important concept in biochemistry. We integrate the mathematical concept of probability with biochemically relevant process of AA ionization. We visualize the ionization process with Mathematica software discussing intramolecular interactions between weakly acidic/basic functional groups and charge--pH variation of amino acids in water solution. The visualizations rely on the notion of probability of ionization of functional groups and demonstrate how the extent of ionization and charge varies with pH of the solution. The examples described include amino acids and weak diprotic acids and bases. The aim is to help students better appreciate the importance and consequences of AA ionization and correct some misconceptions.