The probability of selecting a student from the Acers on the first try is 78/400 = 0.195.
Since the computer program allows for the same student to be selected twice, the total number of students in the school remains 400 even after the first selection.
Since the principal already selected one student from the Acers on the first try, there are now only 77 students left in the Acers.
Therefore, the probability of selecting another student from the Acers on the second try is 77/400 = 0.1925.
So, the probability she will draw the name of another student from the Acers on the second try is 0.1925.