I store my journal papers in a folder, ordered alphabetically by the name of the first author. Assume that each paper has two authors, ordered alphabetically. Assume also that each author name is generated randomly, so that given any letter of the alphabet, there is a 1/26 chance that an author's name starts with that letter (we generate the authors' names first independently, and then order them alphabetically).
Let $A^*$ be the number of papers in my folder where the first author's name starts with the letter A, and $B^*$ be the number of papers in my folder where the first author's name starts with the letter B.
As the number of papers I put in my folder tends to infinity, what is the expected value of the ratio $A^*:B^*$?
One may also ask, if we define $C^*, D^*,E^*$ analogously, what is the ratio $A^*:B^*:C^*:\ldots:Z^*$?